In this talk I will share my experiences teaching in the Bachelor on Data Science program of CY Cergy Paris University. Created in 2018, this program aims to train data scientists with a strong base of mathematics and informatics and hands-on experiences, and is considered to be an incubator for innovative pedagogies within the university.
Teaching in this program meant transitioning from a classical teaching approach, lecturer-centered, to a more student-centered approach, incorporating in the process new pedagogies, like Project-Based-Learning. The students enrolled are from international and backgrounds, and the teaching experience in the last years was heavily impacted by the COVID-19 pandemic. This resulted in a deep questioning of the teaching practice that I believe will change forever the way we understand the role of the lecturer and the student in higher education.
I hope to share with the audience the challenges, successes and lessons learnt from this experience in the last years.
In the first part of this talk, I will discuss sparsity in data science by looking at two applications. The first in machine learning, where I will briefly introduce supervised classification and neural networks. I will then show how sparsity can be used to prune and compress these networks while retaining or even improving accuracy. The second application involves image segmentation. Here, I will show the role of sparsity in capturing boundaries of salient objects in an image. In the second part of this talk, I will discuss my experience with mentoring undergraduates in research by looking at two case studies. One in segmentation, and the other, in data clustering. Finally, I'll talk a bit about some of my service contributions and how they tie into student affairs and teaching.
https://uci.zoom.us/j/97144933986 Meeting ID: 971 4493 3986 One tap mobile +16699006833,,97144933986#
In this talk, we will review a number of past and ongoing research projects, primarily involving undergraduates, in applied mathematics. The topics span a variety of domains such as, but not limited to, (1) physics, including investigating how surface roughness perturbs magnetic fields in superconductors and experimental studies of negatively buoyant particles flowing in a viscous suspension under gravity; (2) social sciences, including using machine learning to build predictive models for changes within the homeless population of Los Angeles; and (3) biology/medicine, including studying how COVID-19 affects the disabled community and developing an ab initio model to quantify how oligomers of amyloid beta can lead to Alzheimer's Disease. The projects have been carried out through directed research courses and summer REU programs.
https://uci.zoom.us/j/95555638255 Meeting ID: 955 5563 8255 One tap mobile +16699006833,,95555638255# US (San Jose) +13462487799,,95555638255# US (Houston)
I will take you on a journey through my teaching, teaching-related, and other scholarly activities. A special focus will be given to my redesign and implementation of Precalculus courses at Cal State LA, where I am the first point of contact of 3000 students every academic year. The success of this implementation is historic as the pass rate of all the sections was over 87%, 40 percentage points higher than the one before the implementation. My model was borrowed by many other departments at Cal State LA and other campuses of the Cal State system. Two research papers about the best teaching, pedagogical, didactical, and assessment practices that led to this accomplishment, were already published. This implementation also had an important impact on the retention rates at Cal State LA.
The final destination of our journey is my research work on the new generation of Bose-Einstein condensates. With some collaborators, we recently obtained interesting results on a new class of PDEs and opened the door to other contributions in this new field.
https://uci.zoom.us/j/99207816721 Meeting ID: 992 0781 6721 One tap mobile +16699006833,,99207816721# US (San Jose) +13462487799,,99207816721# US (Houston)
In this talk, I will present my YouTube channel Dr Peyam and share some creative ways you can use YouTube in your teaching. I will also mention contributions to diversity, as well as possible undergraduate projects on chemical reactions and (time-permitting) Kolmogorov-type flows.
Binary classification with linear classifiers is a fundamental problem in machine learning with broad applications. Traditionally, this problem focuses on using labeled data to learn a linear classifier, but data is often expensive to label or difficult to acquire. Instead of labeling all data points in a data set, we consider labeling a specially chosen subset of points and ask how well we can accomplish our learning task. To answer this question, we will reformulate this problem into the context of Gaussian spherical tessellations and study geometric properties of such tessellations. This work is joint with Rayan Saab and Eric Lybrand.
Many natural and social phenomena involve individual agents coming together to create group dynamics, whether they are cells in a skin pattern, voters in an election, or pedestrians in a crowded room. Here I will focus on the example of pattern formation in zebrafish, which are named for the dark and light stripes that appear on their bodies and fins. Mutant zebrafish, on the other hand, feature different patterns, including spots and labyrinth curves. All these patterns form as the fish grow due to the interactions of tens of thousands of pigment cells. The longterm motivation for my work is to better link genotype, cell behavior, and phenotype — I seek to identify the specific alterations to cell interactions that lead to mutant patterns. Toward this goal, I develop agent-based models to simulate pattern formation and make experimentally testable predictions. In this talk, I will overview my models and highlight several future directions. Because agent-based models are not analytically tractable using traditional techniques, I will also discuss the topological methods that we have developed to quantitatively describe cell-based patterns, as well as the associated nonlocal continuum limits of my models.
Topological and geometric data analysis (TGDA) is a powerful framework for quantitative description and simplification of datasets & shapes. It is especially suitable for modern biological data that are intrinsically complex and high-dimensional. Traditional topological data analysis considers the geometric features of a dataset, while in practice, there could be both geometric and non-geometric features. In this talk, I will introduce a persistent cohomology based method, enriched barcode to embed the non-geometric features in the topological invariants. I will then talk about a geometric method, unnormalized optimal transport for integrating heterogeneous datasets which is crucial for generating a comprehensive topological perspective for the system of interest. Scientific data often have limited size and high complexity, and a straightforward application of machine learning to raw data could result in suboptimal performances. To tackle this challenge, we integrate the TGDA method designed for biological data with deep learning. This topology-based deep learning strategy achieves top performance on standard benchmarks and D3R Grand Challenges, a worldwide competition series in computer-aided drug design. I will also show several applications of our geometric method to the analysis and integration of single-cell omics data. Finally, I will discuss future directions on data-driven modeling using topology, geometry, and machine learning-based approaches.
For cells to divide, they must undergo mitosis: the process of spatially organizing their copied DNA (chromosomes) to precise locations in the cell. This procedure is carried out by stochastic components that manage to accomplish the task with astonishing speed and accuracy. Recent experimental advances from collaborators with NY State Department of Health provide 3D spatial trajectories of every chromosome in a cell during mitosis. Can these trajectories tell us anything about the mechanisms driving them? The structure and content of this cutting-edge data makes applying common particle trajectory and classical data science ideas difficult to apply. I will discuss progress on developing data science tools for this data and mathematical modeling of emergent phenomena.
Single-cell RNA sequencing (scRNA-seq) enables the collection of rich phenotypic information of individual cells. During this sequencing process, each cell is destroyed, which poses challenges in the analysis of time-course data of heterogeneous populations since cell trajectories need to be computationally inferred. Standard trajectory inference methods approximate the transcriptional spectrum of all time points combined by a graph, not leveraging information about the time-points at which the profiles were captured. The recently proposed Waddington-OT algorithm instead appeals to the theory of optimal transport to infer probabilistic couplings between different time points. First, as an example of the benefits and drawbacks of these methods, I will show how we applied them to a problem in immunology, revealing previously unknown effector state potential of tissue-resident innate lymphoid cells. Second, I will discuss issues with the sample efficiency of optimal transport methods in high-dimensions and two approaches to overcome this problem. The first approach relies on the notion of the transport rank of a probabilistic coupling and I will provide empirical and theoretical evidence that it can be used to significantly improve the rates of estimation of optimal transport distances and plans. The second approach relies on a wavelet regularization and admits near minimax optimal rates for the estimation of smooth optimal transport maps.