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This Week in Mathematics

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Entries for this week: 7
Monday January 27, 2020

Mathematics Colloquium [url]
Inferring a Gene Network in Drosophila Blastoderm
    - Jungmin Han, National Institutes of Health
Time: 3:35 Room: Lov 101
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Abstract/Desc: In this talk, I will talk about imputing missing data with neural networks and inferring a gene network using least absolute deviation (LAD) regression. Fowlkes et al. [1] published a set of gene expressions measured from 6078 Drosophila blastoderm during 6 different time cohorts that spanned the 50 minutes prior to the onset of gastrulation. Out of 95 genes and 4 proteins, only 27 of them had complete temporal information in all the cells. To impute the missing data, we trained and tested neural networks on the genes with complete profile as predictors and the genes with missing profile as targets. We then used LAD regression to infer a gene network that describes the dynamics of genes in the cells. Compared to least squares (LS) regression, LAD regression is less sensitive to outliers in a data set. Thus, the inferred network is a better predictor of the gene dynamics in a majority of cells, than a network inferred using LS regression. Using the gene network, we predicted the effects of a gene knockout on the dynamics of gene evolution. [1] C. C. Fowlkes et al., A Quantitative Spatiotemporal Atlas of Gene Expression in the Drosophila Blastoderm. Cell. 133:364-374, 2008.

Wednesday January 29, 2020

Departmental Tea Time
C is for cookie, and shorthand for C[0,1] w/the sup norm
Time: 3: Room: 204 LOV

Thursday January 30, 2020

Algebra and Its Applications
    - Dave Massey, Northeastern
Time: 3:35pm Room: LOV 104

Financial Mathematics Seminar [url]
Random walks and self-excited Black-Scholes models for option pricing
    - Alec Kercheval, Florida State University
Time: 3:35pm-4:25pm Room: LOV 201
Abstract/Desc: The Black-Scholes option pricing model is well known to be a limit of binomial tree models. What happens if the branching times of the binomial tree are given by a random point process, such as the self-exciting Hawkes process commonly used to model order arrivals in the electronic limit order book that determines the price of the stock? In this case, the limit is a version of the Black-Scholes model based on a time-changed Brownian motion. In certain cases we can explicitly compute the price of a European call option as a function of the accumulated intensity of price changes over the life of the option.

Friday January 31, 2020

Colloquium Tea
Time: 3:00 pm Room: 204 LOV

Machine Learning Seminar [url]
Deep Forward Networks I
    - Sathyanarayanan Chandramouli, FSU
Time: 1:25 pm Room: LOV 102

Mathematics Colloquium [url]
Opportunities and challenges for AI and Math in drug discovery
    - Duc Nguyen , Michigan State University
Time: 3:35 Room: Love 101
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Abstract/Desc: Drug discovery is one of the most challenging tasks in the biological sciences since it requires over 10 years and costs more than 2.6 billion to put an average novel medicine on the marketplace. The abundant availability of biological data along with the flourishing advanced AI algorithms opens a future with great hope for discovering new drugs faster and cheaper. Unfortunately, AI faces an enormous obstacle in drug discovery due to the intricate complexity of biomolecular structures and the high dimensionality of biological datasets. In our lab, these challenges have been tackled mathematically. We have introduced multiscale modeling, differential geometry, algebraic topology, and graph theory-based models to systematically represent the diverse biological datasets in the low-dimensional spaces. Combining these mathematical representations with cutting edge deep neural networks, we arrived at novel models not only perform well on virtual-screening targeting important drug properties but also have the ability to design new drugs at an unprecedented speed. Our team has emerged as a top winner in D3R Grand Challenges, a worldwide annual competition series in computer-aided drug design, in the past few years.

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