2017 Talks
Cellular Control Networks and Their Stability Against Mutations
Lora Weiss
December 4th, 2017 - 5:00 - 5:50pm - RH 306
Abstract
Cellular tissue consists of stem cells and a hierarchy of more differentiated cells. It is constantly in flux, with differentiated cells dying, and stem cells replenishing the removed cells. In order to maintain constant size, cellular processes must be regulated by control networks of intra-cellular signaling. Here we introduce models of control networks and analyze their robustness against cancerous mutations. Beginning with a stable cellular network, we investigate consequences of different types of mutations, and in particular, which mutations cause a stable network to fail. Relevant to the theory of cancer, these network failures may lead to unlimited growth of mutant cell populations. Our analysis reveals that only specific mutations may cause a stable network to fail.
About the Speaker
Lora Weiss is a fourth year PhD student studying mathematical biology relevant to the onset of cancer.
Advisor and Collaborators
Lora's advisor is Natalia Komarova.
Embedding Random Vectors
Jen Bryson
November 13th, 2018 - 5:00 - 5:50pm - RH 306
Abstract
I will discuss the approximation of embedding random vectors in a linear subspace using the Marčenko-Pastur law from random matrix theory.
About the Speaker
Jen Bryson is a fourth year graduate student. She is interested in matrix theory and its application to big data.
Advisor and Collaborators
Jen's advisor is Hongkai Zhao.
Artihmetic and Analytic Local Root Numbers of Elliptic Curves
Ching-Heng Chiu
November 1st, 2017 - 4:00 - 4:50pm - RH 306
Abstract
The root number of an elliptic curve E contains some information about the L-function of E. In this talk, I will introduce the arithmetic and analytic local root numbers of elliptic curves. I will talk about some computations and connections between them as well.
About the Speaker
Ching-Heng is a fourth year graduate student. He received his bachelor’s degree in Mathematics from National Taiwan University. In his free time, he likes to watch NBA games and play board games.
Advisor and Collaborators
Ching-Heng's advisor is Karl Rubin.
Step Two: Transitioning from Graduate School to the Tenure Track
May Mei
May 24th, 2017 - 5:00 - 7:00pm - RH 440R
Abstract
Step one: earn a PhD. Step three: profit! What is step two? I'll guide an informal discussion of my own post-PhD career: deciding what kind of career was right for me, gathering application materials and applying, and transitioning from being a graduate student at a large research university to being an assistant professor at a small liberal arts college.
About the Speaker
I'm an assistant professor at Denison University. Before that, I received my PhD from UC Irvine and my BA from UC Berkeley. That is to say, I've lived in California my whole life before moving to Ohio. It's different here. My favorite thing in the universe is probably a nice meal at a fancy restaurant. But someone I respect greatly told me (over a nice meal at a fancy restaurant) that I need hobbies that aren't eating or drinking. So, more recently, I've taken up running and powerlifting. I work at an undergraduate-only institution, so I'm also pretty into teaching.
Advisor and Collaborators
Mei's advisor while at UCI was Anton Gorodetski.
Counting Simultaneous Core Partitions
Hayan Nam
May 22nd, 2017 - 4:00 - 4:50pm - RH 340N
Abstract
A partition with no hook lengths divisible by a is called an a-core partition. For two coprime numbers a and b, a partition is called an (a,b)-core partition if it is both a-core and b-core partition. It is well-known that the number of a-core partitions is infinite, and Anderson proved the number of (a,b)-core partitions is a rational Catalan number. Inspired by work of Johnson, we give an expression for the number of (a,b,c)-core partitions. This is ongoing work with Jineon Baek and Myungjun Yu.
About the Speaker
Hayan is a 3rd year phD student. Her main interests in math are number theory and combinatorics, especially counting problems and enumerative combinatorics. She likes hanging out with people, watching movies and musicals, and playing tennis.
Advisor and Collaborators
Hayan's advisor in Nathan Kaplan. This is joint work with Jineon Baek and Myungjun Yu.
Multiscale Modeling of the Epithelial-Mesenchymal Transition
Catherine Ta
April 18th, 2017 - 4:00 - 4:50pm - RH 340P
Abstract
Epithelial-mesenchymal transition (EMT) is an instance of cellular plasticity that plays critical roles in development, regeneration and cancer progression. Utilizing a systems biology approach integrating modeling and experiments, we observed that adding the mutual inhibition relationship between Ovol2 and EMT inducer Zeb1 generates a novel four-state system consisting of two distinct intermediate phenotypes that differ in differentiation propensities and are favored in different environmental conditions. We then used mathematical models to show that multiple intermediate phenotypes in the EMT system help to attenuate the overall fluctuations of the cell population in terms of phenotypic compositions, thereby stabilizing a heterogeneous cell population in the EMT spectrum. Lastly, we attempted to bridge the gap between discrete and continuum modeling of the EMT system by incorporating the EMT core regulatory network into our heterogeneous cell population dynamics model to create a multiscale EMT model. Our model can capture the larger-scale population growth dynamics while acknowledging the intracellular interactions between proteins within each individual cell. This talk is aimed at a general audience.
About the Speaker
Catherine is a sixth year PhD candidate in Mathematics at UC Irvine, specialized in modeling biological systems. She obtained her B.S and M.S in Mathematics from UC Irvine. When she is not studying Math, she can be found unabashedly taking pictures of her cats and posting them on Instagram.
Advisor and Collaborators
Catherine's advisor is Qing Nie.
Slopes of Two Generalizations of the Artin-Schreier-Witt Towers
Rufei Ren
April 10th, 2017 - 4:00 - 4:50pm - RH 340N
Abstract
Let p be a prime number. The Artin-Schreier-Witt tower delt in [DWX] is defined by a single variable polynomial f(x) ∈ F p which is a tower of curves ⋅ ⋅ ⋅ → C m → C m-1 → ⋅ ⋅ ⋅ → C 0 =A 1 , with total Galois group Z p . In [DWX], Davis, Wan and Xiao showed that when the conductor m χ of a character χ is large enough, the slopes of NP( f , χ ) L form arithmetic progressions which are independent of m χ . We mainly studied its two generalizations.
About the Speaker
Rufei is a 5th year in the math department. He enjoys both watching and playing DOTA games in his free time.
Advisor and Collaborators
Rufei's advisors are Karl Rubin and Liang Xiao.
Stochastic Modeling of Stem Cells
Jay Yang
March 1st, 2017 - 3:00 - 3:50pm - RH 440R
Abstract
We are interested in determining the most likely control network(s) that govern the regulation of human colon crypt stem cell lineages, where lineages are comprised of stem cells, transit amplifying cells, and differentiated cells. We started with a theoretically known set of 32 smallest control networks compatible with tissue stability. We proposed and implemented an algorithm of tests where we compared the networks' simulated behavior with the measured observations, and we discovered only 3 candidate networks that are most compatible with the measurements.
About the Speaker
Jay is a 6th year in the math department. He is a value-driven mathematician/statistician with a focus on Data Science and Computational Biology. He is passionate about solving complex problems and integrating knowledge and skills into practical applications.
Advisor and Collaborators
Jay's advisor is Natalia Komarova.
