A. Ali Heydari
University of California, Merced
I'm a mathematician and a computer science enthusiast. I do random development projects (algorithms, websites, apps, etc.) when I need a break from math. I really enjoy solving puzzles and discovering new things, hence being a mathematician and a developer. Currently, I am an Applied Mathematics Ph.D. student and a graduate research assistant at UC Merced. I am very interested in machine learning (deep learning, multi-task learning and transfer learning in particular), Computer Vision, bioinformatics and mathematical algorithms for big data and artificial intelligence.
The goal of my current research is to employ multi-scale mathematical models towards the study of biological diseases, in particular, prion disease and cancer. My current research focuses on using data, mainly Single-Cell RNA Sequencing Data (sc-RNA seq) to model the lineage trajectory of cells in order to understand its fate ( which can be very useful in disease progression and treatment options) using a mapping of gene expression to spatial coordinates on a tissue. Another aspect of my research will be to use generative models, such as our novel VAE/GAN hybrid (as used in our novel super-resolution framework SRVAE), to generate synthetic single-cell data. Creating this synthetic data will help scientists with more robust analysis and more reproducible research.
My single-cell research will be coupled with the use of other data such as genetic and epigenetic data, to model the progression disease in order to better predict the effectiveness/optimality of drugs, treatments or a combination of both based on the cancer type. So far as preliminary work during the NSF NRT-ICGE fellowship, our team has been able to develop a machine learning model that will predict Breast Cancer patients' treatment outcomes given their genetic mutation profile. This work is done with my mentors and advisors Dr. Ben Brown, Dr. Petrus Zwart, and Dr. Suzanne Sindi.
Both cancer and prion diseases are epigenetic processes – where the disease is transmitted vertically during cell division and the disease agent is encoded by the host cell itself. The future direction of my research is to understand the genetic basis of fatal diseases, such as cancer, Alzheimer’s and Creutzfeldt-Jakob, using a combination of mathematical modeling (PDEs, ODEs) and data analysis techniques (machine learning and statistics). In the past few months, I have been working with my advisor, Dr. Suzanne Sindi, and Dr. Maxime Theillard to develop a model of prion protein transmission in a dividing yeast cell. We considered the prion protein concentration as a distribution in a three-dimensional yeast cell and modeled the cell-wall dynamics during division with the level set method. While still early, my work is demonstrating features of asymmetric protein segregation known to be important during disease transmission. Compared to my work thus far in yeast cell modeling, cancer cells are far more complicated both in the structure of their cellular properties (rigid cell-walls compared to flexible cell-membranes) and intracellular dynamics.
During my various internships, I have worked on other machine learning projects, such as Super Resolution Variational Autoencoder (SRVAE) and Adaptive Learning Integration (ALI). SRVAE is a novel framework for single image super-resolution which is much faster and more stable to train than most Generative Adversarial Networks (GANs). ALI is a novel optimization package used for multi-part loss functions which will 1) help accelerate the convergence of the network and 2) it will avoid the divergence due to bad learning rates. More about both of these projects could be found on my MACHINE LEARNING page.