CockTales

Last week I participated in a show addressing sexual violence called CockTales, written and produced by Whitney Mackman. The show was originally conceived as a counterpoint to the Vagina Monologues, with the spin being that participants read a collection of monologues and dialogues mostly written by men that address toxic masculinity and its role in theContinue reading “CockTales”

Invasion Probabilities paper accepted

Congratulations to Becky Borchering! The research paper stemming from the second chapter of her dissertation was accepted today. This paper has a fun working title that we always joke about in the Stochastics Lab. Originally, we expected this to be an easy project — almost too trivial to write up as a research article. IContinue reading “Invasion Probabilities paper accepted”

Online resource: The Analysis of Data

This came across my desk this morning: theanalysisofdata.com. The author is former professor of Computer Science named Guy Lebanon, who is now, according to his website the Director of Product Innovation at Netflix.  The text appears to be very rigorous and is notable because he goes all the way from first principles to Limit TheoremsContinue reading “Online resource: The Analysis of Data”

Stem Cell Paper Accepted

Congratulations are in order for Vin Cannataro today.  The research paper stemming from the second chapter of his dissertation was accepted today by Evolutionary Applications. The Evolutionary Trade-off between Stem Cell Niche Size, Aging, and Tumorigenesis Vincent L. Cannataro, Scott A. McKinley, Colette M. St. Mary http://biorxiv.org/content/early/2016/06/15/059279 Many epithelial tissues within large multicellular organisms areContinue reading “Stem Cell Paper Accepted”

Stochastics and Movement in Living Systems

The last twenty years have seen a revolution in tracking data of biological agents across unprecedented spatial and temporal scales. An important and ubiquitous observation from these studies is that path trajectories of living organisms are often poorly described by the universality class of stochastic models broadly represented by classical Brownian motion. To abuse aContinue reading “Stochastics and Movement in Living Systems”

Homework 4, due Friday Oct 24

Jacod and Protter, problems 11.5, 12.4 and 12.11 11.15 Let be a continuous distribution function and the  be uniform on . Define . Show that has distribution function . 12.4 Let denote the correlation coefficient for . Let , and . Show that . (This is useful because it shows that is independent of theContinue reading “Homework 4, due Friday Oct 24”

Probability Theory, Homework 3, due Friday Oct 3.

From Jacod and Protter 9.5  Let be a probability space. Suppose that is a random variable with almost surely and . Define by . Show that defines a probability measure on . 9.7 Suppose that and let be defined as above. Let denote expectation with respect to .  Show that . Further exercises Exercise 3.Continue reading “Probability Theory, Homework 3, due Friday Oct 3.”

Probability Theory: Homework 2

Exercises, due Wed Sept 17. Jacod and Protter: 4.1, 5.20 and 7.11 4.1 (Poisson Approximation to the Binomial) Let be a Binomial probability with probability of success and the number of trials . Let . Show that Let and let change so that remains constant. Conclude that for small and large , , where .Continue reading “Probability Theory: Homework 2”

Probability Theory: Homework 1

Exercises, due Wed Sept 3. From Jacod and Protter, problems 2.6, 2.7, 2.10 and 2.14. 2.6 Let be a -algebra of subsets of and let . Show that is a -algebra of subsets of .  Is this still true if is a subset of that is not a member of ? 2.7  Let be aContinue reading “Probability Theory: Homework 1”