Summer 2021

Deciding (TBD soon)

Summer 2020

Summer 2019



Spring 2019


Fall 2020

Summer 2018

Summer 2017

Summer 2015

A. Ali Heydari

Ph.D. Student 

Applied Mathematics

University of California, Merced

I am, by training, a mathematician and a computer scientist. 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. According to the National Cancer Institute, cancer is the second cause of death in the United States with approximately 606,520 lives lost annually. One promising avenue in treating cancers is immunotherapy, getting the body’s immune system to act against the cancer cells. While immunotherapy has been successful for some patients, many remain non-responsive due, in part, to the individual mutations in their specific cancer type. Recent discoveries on cancer complexity have triggered a shift away from a one-size-fits-all approach toward personalized treatments. Scientists can now measure the gene expression in each cell of a tumor via single-cell RNA-sequencing, which yields unprecedented resolution. Unfortunately, a fundamental problem in cancer gene expression research is the low number of single-cell observations of each cancer subtype, mostly due to a lack of available samples, experimental costs, or ethical reasons. The absence of sufficient data causes a majority of current treatment prediction models to lack accuracy and generalizability. Recently, researchers have focused on using deep generative models to produce realistic single-cell data, but these mathematical models solely depend on gene expressions and do not take into account the spatial components of tissues, which is crucial in understanding the heterogeneity in the tumor microenvironment.

A main issue in single-cell analysis remains the inability to harness sequencing data from different laboratories, even if all experimental setups were the same. Due to the lack of direct comparison between the existing data, researchers need to spend time and resources generating their own data, often in large quantities to allow for meaningful downstream analysis (such as classification and clustering). There is an unmet need for a framework that allows the transfer of existing knowledge to the post-experiment analysis of new sequencing data. Such a model will not only allow for fewer number of experimental samples, but it can yield more accurate results by leveraging the knowledge learned from existing data. We hypothesize that training a deep neural network with spatially informed synthetic data (in addition to the existing public datasets) will result in a transferable model that can be fine-tuned for domain-specific applications with relatively few samples. My PhD research aims to use deep learning and mathematical modeling to address these problems in cancer immunology.

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.

© 2020 A. Ali Heydari