David's illustrations have been published in Science, Physical Review Letters, Molecular Pharmaceutics, Biosensors and Bioelectronics, and the Proceedings of the National Academy of Sciences.
University of California, San Francisco
Postdoc, 2010-2012
Tlsty Lab
Harvey Mudd College
BS, Physics, 2005
Advisor: Robert J. Cave
A mathematical way to think about biology comes to life in this lavishly illustrated video book. After completing these videos, students will be better prepared to collaborate in physical sciences-biology research. These lessons demonstrate a physical sciences perspective: training intuition by deriving equations from graphical illustrations.
"Excellent site for both basic and advanced lessons on applying mathematics to biology."
-Tweeted by the U.S. National Cancer Institute's Office of Physical Sciences Oncology
This is not a quick fix: It can take a couple months to work through this material at a comprehensible pace. We briefly review algebra and calculus, describe basic probabilistic modeling, explain how to solve dynamical systems, and then present an area of application in physical oncology. Even after viewing these sections, students will still need to invest significant effort in order to participate in multidisciplinary research. These videos provide starting points for conversation between biological and physical disciplines. Students may wish to return to these tutorials periodically for review as research proceeds.
(PowerPoint files and backup links to videos, in case the udemy versions experience technical difficulties, available at main website lookatphysics.com)This video outlines contents from the course
What is a number? More specifically, what is a distinguishable counting manipulative?
Street numbers, money in bank accounts, points on number lines, and quantum particles as contrasted with distinguishable manipulatives For our purposes, infinity is not a number
Variables: at once arbitrary, yet specific and particular
Functions: composition and inverses
Imaginary number, square-root of -1
Graphical and analytic understanding of solving the quadratic equation
Plotting quadratic functions
Completing the square
Flat space, curved space, non-embedded curved space
Pythagorean theorem (ca. 300 BCE)
Gauss summation trick, which is used when counting the number of pairwise interactions in a population of components
How many ways can we arrange n distinct objects in n slots? The answer is n (n - 1) (n - 2) . . . 3 * 2 * 1. Because this kind of calculation appears often in the study of probabilities, we give it a symbol called the factorial: n! = n (n - 1) (n -2) . . . 3 * 2 * 1.
ε-δ definition of limit, notion of "arbitrarily close" Example of calculating a limit Limits do not always exist
The goal of this and the next 4 videos is to formalize an idea of "slope" and then to build a cribsheet of rules for studying the slopes of some example functions. In this video, we define the derivative, caution against interpreting differentials as numbers, and remark that derivatives do not always exist. It is important to become familiar with derivatives because they provide a basic vocabulary for talking about dynamical systems in the natural sciences (including in biology).
When a function depends on multiple independent variables, the "partial" symbol is reserved to denote slopes calculated by jiggling one independent variable at a time
This set of four videos introduces power series representations. Using a power series representation is like using decimal representation. Both techniques organize the description of the target object at levels of increasing refinement.
In this first video, we show that the second derivative corresponds to the curvature of a plot. In this way, we strengthen intuition that higher-order derivatives can also have geometric interpretations.
In these four videos, we develop a familiar with integration that will later be useful for deducing functions of time (e.g. number of copies of a molecule as a function of time) using rates of change (e.g. the first derivative of the number of copies of a molecule with respect to time). In this first video, we develop the concept of the definite integral in terms of the area under a curve.
Two wrongs make a right Tear two differentials apart as though they retained meaning in isolation Slap on the smooth S integral sign as though it were a unit of meaning itself, even without a differential You get the same integral expression you would obtain long-hand using u-substitution or "change of variables" in integrals
Compounding interest with arbitrarily small compounding periods
Power series representation of exp(x)
exp(0) = 1
(exp(x))^p = exp(px)
exp(x)exp(y) = exp(x+y)
Mnemonic for memorizing e = 2.718281828459045...
The natural logarithm is the inverse of the exponential
The indefinite integral of 1/x is ln(x) + C
Various notions related to stochasticity are involved in many homework problems from undergraduate courses in calculus and differential equations * For-real stochasticity: Fundamental indeterminism * Fake stochasticity: Periodic, deterministic hidden variables * Fake stochasticity: Aperiodic, deterministic (chaos) Markov models
This is a canonical worked problem from introductory systems biology (Alon, Ch. 2.4, pp. 18-21). We will explain one way to fantasize about the classic protein dynamics equation dx/dt = beta - alpha x and analytically demonstrate that protein "rise time" depends on degradation rate only.
Using a collision picture to understand why reaction rates look like polynomials of reactant concentrations
Cooperativity of a simple (oversimplified) kind
How Hill functions, considered in combination with linear degradation, can support bistability
Collisional population dynamics and tabular game theory An outcome of the prisoner's dilemma is simultaneous survival of the relatively most fit with decrease in overall fitness
Distributions, averages, variances, useful identities
Statistical independence
Routinely-exploited expressions: Covariances vanish and variances of sums are sums of variances
Bernoulli (ca. 1700s) coin-toss process Independent events
Independent + "rare" events
Approximation for n! for large n
Comparison with integral of natural logarithm
Many independent events
Binomial distribution in limit of many coin tosses
Gaussian distribution
Physics: Taylor expansion in the context of tightly-controlled, narrow instrument noise
Biology: Logarithm of product of fluctuating factors: Log-normal distributions
Standard deviation vs. sample standard deviation
Mean vs. sample mean
Standard deviation of the mean vs. standard error of the mean
"I quantitated staining intensity for 1 million cells from 5 patients, everything I measure is statistically significant!" It is quite possible that you need to use n = 5, instead of 5 million, for the √ n factor in the standard error.
Reduced chi-square χ2 fitting
Normalized residuals
Dynamics of population fractions
Model: RNA polymerase makes many (usually unsuccessful) independent attempts to initiate transcription. Once a mRNA strand is produced, it begins to make independent (usually many unsuccessful) attempts to be degraded.
Outcome: As in part a, mRNA copy numbers are Poisson distributed
Relative dominance in a population is determined, not merely by "fitness" alone, but also depends on the degree to which individuals "breed true."
CAUTION: I'm not familiar enough with numerical integration to know whether the particular example of the method for step-size adaptation in the video is used generally (or at all) in commonly available software packages. The purpose of the example was to show that it is possible to generate an error estimate (a) without knowledge of the actual solution and (b) by comparing the solutions from two numerical integration algorithms.
Linear analysis of almost linear systems
Intuitive introduction to 2-d oscillations (Romeo and Juliet)
Twisting nullclines
Time-delays
Stochastic resonance
This video abstract highlights two recent papers from authors at the University of California, San Francisco working within the Princeton Physical Sciences Oncology Center
Liao D, Estévez-Salmerón L, and Tlsty T D 2012 Conceptualizing a tool to optimize therapy based on dynamic heterogeneity† Phys. Biol.9(6):065005 (doi:10.1088/1478-3975/9/6/065005) (open-access online)
Liao D, Estévez-Salmerón L, and Tlsty T D 2012 Generalized principles of stochasticity can be used to control dynamic heterogeneity Phys. Biol.9(6):065006 (doi:10.1088/1478-3975/9/6/065006) (open-access online)
† The authors dedicate this paper to Dr Barton Kamen who inspired its initiation and enthusiastically supported its pursuit.
The research described in these articles was supported by award U54CA143803 from the US National Cancer Institute. The content is solely the responsibility of the authors and does not necessarily represent the official views of the US National Cancer Institute or the US National Institutes of Health.
(C) 2012-2013 David Liao (lookatphysics.com) CC-BY-SA (license updated 2013 March 27). When distributing this video under the Creative Commons license, please cite the full journal references above (including authors and dois) as well as the citation information for this video:
Title: Dynamic heterogeneity for the physical oncologist
Author of work: David Liao
The full citation of the papers (at least the
first paper) is necessary because the journal Phys. Biol. has
released these works under a CC-BY-NC-SA license. These papers are copyrighted
and not public domain.
Simple lattice model
Winner takes all
Nowak and May 1992
Por favor escribe tu crítica aquí
I am very interested in the course but as a biologist I had little maths during my education years. I only have school level maths & it is now very rusty. The lectures are very fast with little to no explanations, if you get struck up.
May be others are more familiar with maths required here so it is easier for them. From my point of view the course could be divided into two or three parts & more examples should have been included to make it more intuitive. The language used is really hard to understand. It is very technical.
I love this guy. He's giving me a terrifec mathematical backgound and overview that I can handle.
Good organization.
Good explanation.
Good pronunciation.
I like it
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