OSU PROBABILITY SEMINARDepartment of Mathematics |
Day/Time/Room |
Speaker |
Title and abstract |
Tuesday, October 10, 4:00 pm BEXL 207 |
Yevgeniy Kovchegov
Oregon State University |
"Random self-similar trees: dynamical pruning and its applications to inviscid Burgers equations" Abstract. We introduce generalized dynamical pruning on rooted binary trees with edge lengths. The pruning removes parts of a tree T, starting from the leaves, according to a pruning function defined on subtrees within T. The generalized pruning encompasses a number of previously studied discrete and continuous pruning operations, including the tree erasure and Horton pruning. For example, a finite critical binary Galton-Watson tree with exponential edge lengths is invariant with respect to the generalized dynamical pruning for arbitrary admissible pruning function. We will discuss an application in which we examine a one dimensional inviscid Burgers equation with a piece-wise linear initial potential with unit slopes. The Burgers dynamics in this case is equivalent to a generalized pruning of the level set tree of the potential, with the pruning function equal to the total tree length. We give a complete description of the Burgers dynamics for the Harris path of a critical binary Galton-Watson tree with i.i.d. exponential edge lengths. This work was done in collaboration with Ilya Zaliapin (University of Nevada Reno) and Maxim Arnold (University of Texas at Dallas). |
Tuesday, October 31, 4:00 pm BEXL 207 |
James Watson
CEOAS, Oregon State University |
"Anticipating and Managing Risk in Marine Social-ecological Systems" Abstract. In this presentation I introduce a new approach to managing risk in marine food-producing systems -- fisheries and aquaculture -- based on weather index and cooperative insurance. The mathematical framework is explained and then results are shown from its application to a case-study in Myanmar, where empirical data has been collected. I will also briefly introduce early work from a new project focusing on Manifold Learning, a new approach to studying the multilevel dynamics of complex systems. |
Tuesday, November 21, 4:00 pm BEXL 207 |
Ed Waymire
Oregon State University |
"When 4th Moments Are Enough" Abstract. This talk concerns a somewhat innocent question motivated by an observation concerning the use of Chebyshev bounds on sample estimates of p in the binomial distribution with parameters n, p. Namely, what moment order produces the best Chebyshev estimate of p? If S_{n}(p) has a binomial distribution with parameters n, p, then it is readily observed that argmax_{0 ≤ p ≤ 1}ES_{n}^{2}(p) = argmax_{0 ≤ p ≤ 1}np(1-p) = 1/2, and ES_{n}^{2} = n/4. Rabi Bhattacharya observed (personal communication) that while the second moment Chebyshev sample size for a 95% confidence estimate within ±5 percentage points is n = 2000, the fourth moment yields the substantially reduced polling requirement of n = 775. Why stop at fourth moment? Is the argmax achieved at p = 1/2 for higher order moments and, if so, does it help, and can one easily compute the moment bound ES_{n}^{2m}(1/2)? As captured by the title of this talk, answers to these questions lead to a simple rule of thumb for best choice of moments in terms of an effective sample size for Chebyshev concentration inequalities. This talk is based on joint work with Chris Jennings-Shafer and Dane Skinner. |
Tuesday, January 23 (Winter'18), 4:00 pm TBA |
Sidney Resnick
Cornell University |
TBA Abstract. TBA |