Dr. McLay on Punk Rock Operations Research posted the following exam question she gave to a stochastic processes class:
Question: There is a zombie outbreak in Richmond. The zombie population can be modeled as a linear growth birth death process. Each zombie independently reproduces at a rate of λ = 2/hour and is killed by resourceful Virginians at a rate of μ = 0.5/hour. If the population started with a pack of two zombies, find the average size of the zombie population after 24 hours.
Answer: The average size of the population can be modeled using a linear growth birth death process. Let Ei denote the expected size of the zombie population after 24 hours given that there are initially i zombies. Then Ei = i * E1.
The expected size of the zombie population is given by
Ei = ie^((λ-μ)t) = 2*e^36 after t=24 hours. That is a lot of zombies!
Math is cool. There are some assumptions that go into this solution that are addressed in her post.
Optimal Shoelacing
This [lacing shoes] is of course an instance of a Traveling Salesman Problem (TSP). Each lace hole represents a city which can be visited exactly once. For example, the slack is maximized by finding the shortest tour, while the slack can be minimized by finding the longest Hamiltonian circuit. Of course, my daughter would prefer finding a good balance between these two extreme solutions, while also ensuring that tightening and loosening the laces are relatively easy to perform. The former objective can be equivalently specified in terms of minimizing deviation from a desired tour length, while the latter requirement can perhaps be approximated by eliminating unfavorable connection patterns and reducing overall friction.
To succeed in business, one needs to be smart—really smart—but business intelligence (BI) is not measured by college degrees. BI is about quickly making sense of the vast amounts of data collected about all dimensions of a business, and then making sound decisions that will generate value for the company. For business schools, it’s also a big opportunity, one that is, by and large, being missed.
expose-the-light:
Sun’s Twin Discovered — the Perfect SETI Target?
There are 10 billion stars in the Milky Way galaxy that are the same size as our sun. Therefore it should come as no surprise that astronomers have identified a clone to our sun lying only 200 light-years away.
Still, it is fascinating to imagine a yellow dwarf that is exactly the same mass, temperature and chemical composition as our nearest star. In a recent paper reporting on observations of the star — called HP 56948 — astronomer Jorge Melendez of the University of San Paulo, Brazil, calls it “the best solar twin known to date.”
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![Optimal Shoelacing
This [lacing shoes] is of course an instance of a Traveling Salesman Problem (TSP). Each lace hole represents a city which can be visited exactly once. For example, the slack is maximized by finding the shortest tour, while the slack can be minimized by finding the longest Hamiltonian circuit. Of course, my daughter would prefer finding a good balance between these two extreme solutions, while also ensuring that tightening and loosening the laces are relatively easy to perform. The former objective can be equivalently specified in terms of minimizing deviation from a desired tour length, while the latter requirement can perhaps be approximated by eliminating unfavorable connection patterns and reducing overall friction.](http://24.media.tumblr.com/tumblr_m3eq423g2K1qbby7no1_250.gif)
