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Research Seminars: Probability and Statistics


Past Probability and Statistics:

Spring 2019

Time & Location: All talks are on Wednesdays in Gibson Hall 126 at 3:00 PM unless otherwise noted.
Organizer: Scott McKinley and Swati Patel

 


January 11

Influence of Receptor Recharge on the Statistics of Captured Particles

Greg HandyUniversity of Utah

Abstract:

We consider a setup where particles are released into a domain and diffuse freely. Part of the boundary is absorbing, where the particles can escape the domain, another part is reflecting. The rest of boundary consists of capture regions that switch between being reflecting and absorbing. After capturing a particle, the capture region becomes reflecting for an exponentially distributed amount of time. This non-zero recharge time correlates the particles' paths, complicating the mathematical analysis of this system. We are interested in the distribution of the number of particles that are captured before they escape.

Our results are derived from considering our system in several ways: as a full spatial diffusion process with recharging traps on the boundary; as a continuous-time Markov process approximating the original system; and lastly as a system of ODEs in a mean-field approximation. Considering the full spatial diffusion process, we prove that the total expected number of the captured particles has an upper-bound of the order of log n.  We then apply our approximations to investigate time courses for the expected number and higher ordered statistics of captured particles. We find that the amount of variation observed in the total number of captured particles varies non-monotonically with the mean recharge time. Lastly, we combine these results together to predict stochastic properties of intracellular signals resulting from receptor activation.


January 30

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SpeakerInstitution

Abstract: TBA



February 6

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February 13

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Chris MilesNYU

Abstract: TBA


February 20

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February 27

May have trouble getting a Hotel room.  Mardi Gras

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March 6

Spring Break

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March 13

A non-central limit theorem on heavy-tailed chaos

Ray BaiInstitution

Abstract:

We introduce the partial-sum limit theorems for a class of stationary sequences exhibiting both heavy tails and long-range dependence. The stationary sequences are constructed using heavy-tailed multiple stochastic integrals and conservative null dynamical systems. The limits are represented by multiple stables integrals, where the integrands involve the local times of the intersections of stationary stable regenerative sets. This is a joint work with Takashi Owada and Yizao Wang.


March 20

Recent issues and discoveries on stochatically modeled reaction networks

Jinsu KimUC Irvine

Abstract:

Abstract :


A reaction network is a graphical configuration that describes an interaction between species (molecules). If the abundances of the network system is small, then the randomness inherent in the molecular interactions is important to the system dynamics, and the abundances are modeled stochastically as a jump by jump fashion continuous-time Markov chain. One of challenging issues facing researchers who study biological systems is the often extraordinarily complicated structure of their interaction networks. Thus, how to characterize network structures that induce characteristic behaviors of the system dynamics is one of the major open questions in this literature. In this talk, I will provide recent issues and discoveries on stochastically modeled reaction networks. Specifically, we will focus on existence of stationary distributions and the convergence rate for the process to its stationary distribution.

March 27

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Ilya TimofeyevUniversity of Houston

Abstract: TBA


April 3

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Farzad SabzikarInstitution

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April 10

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April 17

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April 24

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May 1

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May 8

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Mathematics Department, 424 Gibson Hall, New Orleans, LA 70118 504-865-5727 math@math.tulane.edu