2015 Talks
Mathematical Modeling of Learning from an Inconsistent Source: A New Approach
Timmy Ma
November 25th, 2015 - 4:00 - 4:50pm - RH 440R
Abstract
Continuing the discussion of how children can modify and regularize linguistic inputs from adults, we study the key features of the regularization of language. We present a new interpretation of existing algorithms to model and investigate the process of a learner learning from an inconsistent source. Our model allows us to analyze and present a theoretical explanation of a frequency boosting property, whereby the learner surpasses the fluency of the source by increasing the frequency of the most common input.
About the Speaker
Timmy is in his 4th year of the program. He is a mathlete and loves to play all kinds of sports. His Jedi master was Yoda and he joined the Dark Side a little over two years ago to help the Empire take control of the Galaxy.
Advisor and Collaborators
Timmy's advisor is Natalia Komarova.
Methods for Defining Color Categories
Nikki Fider
November 23rd, 2015 - 4:00 - 4:50pm - RH 340N
Abstract
In the fields of psychology and linguistics, it is understood that speakers from a common linguistic background agree to use certain basic color words to divide the color space--for example, we agree to use "red" and not "sanguine". The study of how distinct cultures categorize the color space offers insight into human perception and communication. This talk outlines mathematical methods which aim to separate basic color words from non-basic color words. Furthermore, we provide a way to identify which regions of the color space correspond to each basic color word. The analysis and examples we provide will be based on data provided by the World Color Survey, which has color identification data from 110 (mostly non-industrialized) cultures.
About the Speaker
Nikki is a 4th year graduate student working under Dr. Natalia Komarova. Nikki has an awesome dog named Harley who keeps her company while she does her research and school work, even though Harley can be very distracting sometimes. They enjoy fine dining (In-n-Out!), long walks on the dog beach (no leashes!), and the the BBC version of Pride and Prejudice (Colin Firth!).
Advisor and Collaborators
Nikki's advisor is Natalia Komarova.
Markovian Modeling of Credit Risk
Ali Kassir
November 17th, 2015 - 5:00 - 5:50pm - RH 440R
Abstract
Credit ratings have been an important variable in the measurement and management of credit risk. In this talk I will present a Markovian model of credit risk that takes into account an individual's migration between different credit ratings. I will also discuss the portfolio case and introduce a model for the correlation that takes place in a portfolio. I will present a way of measuring the associated Value at Risk and using it to set interest rates. Finally, I will present some results using data.
About the Speaker
Ali is a 5th year graduate student at UC Irvine. He obtained his B.S. and M.S. in Mathematics from UC Irvine. Ali enjoys road trips with his wife and 9.5 month old son.
Advisor and Collaborators
Ali's advisors are Knut Solna and Patrick Guidotti.
Deformation Quantization of Vector Bundles on Lagrangian Subvarieties
Taiji Chen
May 27th, 2015 - 4:30 - 5:20pm - RH 440R
Abstract
We give a necessary and sufficient condition for a line bundle to be supported on a smooth Lagrangian subvariety of an algebraic symplectic variety. This uses the method of formal geometry, involving formal power series with a non-commutative product. We try to generalize this result to vector bundles by using the language of Maurer-Cartan space, which is a generalization of Lie algebra cohomology.
About the Speaker
Taiji received his Bachelor's degree in Mathematics from the Capital Normal University in China, and now he is working on algebraic geometry, under the guidance of Professor V. Baranovsky. In his free time, Taiji enjoys playing violin and studying music theory by using mathematics.
Advisor and Collaborators
Taiji's advisor is Vladimir Baranovsky.
A Mathematical Model for Metabolic Patterning in Colon Cancer
Mary Lee
April 22nd, 2015 - 4:00 - 4:50pm - RH 440R
Abstract
Understanding how cancer cells metabolize nutrients into energy is an important step toward developing treatment methods for this disease. In this talk I will present experimental data for a symbiotic relationship between two different metabolic cell types in colon cancer. I will present a mathematical model that describes this relationship as a Turing pattern based on the Wnt signaling pathway, an important pathway in the healing and development of cells. I will discuss how interfering with Wnt signaling alters the metabolic pattern, and show that the mathematical model agrees with these observations. Finally, I will discuss how the model can be used to simulate treatment programs that take advantage of this symbiotic relationship and show that they have the potential to be highly effective. This talk is aimed at a general audience.
About the Speaker
Mary is a 6th year graduate student at UC Irvine. She obtained her B.A. in Applied Mathematics from UC Berkeley and her M.S. in Mathematics from UC Irvine. She worked as Senior Systems Engineer at Raytheon Space and Airborne Systems before coming to UCI and is currently an Adjunct Employee at the RAND Corporation. Mary enjoys wearing her Viking helmet while looking up and off into the distance, with waves from an angry sea crashing behind her.
Advisor and Collaborators
Mary's advisor is John Lowengrub.
Quasicrystals, Labyrinth Model, and Product of Two Cantor Sets
Yuki Takahashi
April 8th, 2015 - 4:00 - 4:50pm - RH 440R
Abstract
We will talk about one and two dimensional quasicrystals, and will see how questions on quasicrystals lead naturally to questions on hyperbolic dynamics. We will also discuss the Labyrinth model, which is a two dimensional quasicrystal model, and will show that the spectrum of this model, which is known to be the product of two Cantor sets, becomes an interval for small values of the coupling constant.
About the Speaker
Yuki received a Bachelor's degree in Mathematics from the University of Tokyo, and now he is working on Dynamical System and Mathematical Physics, under the guidance of Professor A. Gorodetski. In his free time, Yuki enjoys juggling, and practicing yoga in the ARC.
Advisor and Collaborators
Yuki's advisor is Anton Gorodetski.
