Modeling and analysis of zebrafish-skin patterns

Speaker: 

Alexandria Volkening

Institution: 

Northwestern University

Time: 

Thursday, January 14, 2021 - 2:00pm to 3:00pm

Host: 

Location: 

ZOOM

 

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.

 

Recording: https://uci.zoom.us/rec/share/hvSPwIkuv-IR_vXmMhVLL1Q9j_eYeOwTQeIfOHwLJIJIHJmiuYtYOrTWw9d6qinG.G0mfFaRfGuNNy20x

Topological and Geometric Data Analysis Meets Data-driven Biology

Speaker: 

Zixuan Cang

Institution: 

UCI

Time: 

Tuesday, January 12, 2021 - 2:00pm to 3:00pm

Host: 

Location: 

ZOOM

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.

Recording: https://uci.zoom.us/rec/share/xws5VA8hg1OIwEl6_HHDH9Mv9zcYr4hFeQWUV_31H6_SUXxfY8_ydAPLq5CsrwJ1.vtG9oi8HXrUU4EDS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Modeling & data science of stochastic organization in the mitotic spindle

Speaker: 

Christopher Miles

Institution: 

NYU

Time: 

Wednesday, January 13, 2021 - 2:00pm to 3:00pm

Host: 

Location: 

ZOOM

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.

Recording: https://uci.zoom.us/rec/share/8MTz98Ak8qoyhL9xcU_jhzkep6HtuJX3KEn--tP_8cyimA2vC6hdToCcrDNuf-au.MSurylc-yjnGGVyD

Inference of gene expression trajectories and statistical optimal transport

Speaker: 

Jan-Christian Hütter

Institution: 

Broad Institute

Time: 

Monday, January 11, 2021 - 2:00pm to 3:00pm

Host: 

Location: 

ZOOM

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.

Recording: https://uci.zoom.us/rec/share/Z7IkY8uyS0-YHDLmTnO4tB9RjZChpdXhumjFk1grXlXWZBRCBFx0dzKGGgM_HRHd.5AmbNeTa0QVWY_Vr

Chaos and emergent computation in biological dynamics

Speaker: 

William Gilpin

Institution: 

Harvard Quantitative Biology Initiative

Time: 

Friday, January 15, 2021 - 2:00pm to 3:00pm

Host: 

Location: 

ZOOM

Experimental measurements of biological systems often have a limited number of independent channels, hindering the construction of interpretable models of living processes. Dynamical systems theory provides a rich set of tools for inferring underlying mathematical structure from partial observations, yet translating these insights to real-world biological datasets remains challenging. In this talk, I will overview my recent work at the intersection of nonlinear dynamics, chaos, and biology. I will first focus on my recent work on developing physics-informed machine learning algorithms that extract dynamical models directly from raw experimental data. I will present a general technique for inferring strange attractors directly from diverse biological time series, including gene expression, patient electrocardiograms, fitness trackers, and neural spiking. Next, I will next discuss my efforts to apply concepts from dynamical systems theory to understand particular biological phenomena. I will describe my work on biological fluid dynamics, and the discovery of a beautiful vortex crystal formed by the swimming strokes of early-diverging animals—which enables a novel feeding strategy based on chaotic mixing of the local microenvironment. I will relate this work to broader questions at the intersection of nonlinear dynamics and organismal behavior. I will conclude by discussing how these insights open up several exciting new avenues at the intersection of dynamical systems theory, systems biology, and machine learning.

 

Recording: https://uci.zoom.us/rec/share/zGBcf-qSd9dD-OVky2kcA1GY5O8D_fnrRbJV5NExHFKq8Fh4do4DyTs6hSPPmyyl.3H4ebSf1h1CXg2z9

Traveling waves and patterns in multiple-timescale dynamical systems

Speaker: 

Paul Carter

Institution: 

University of Minnesota

Time: 

Friday, October 9, 2020 - 4:00am to 5:00am

Host: 

Location: 

ZOOM

Systems with multiple timescales, in which the dynamics separate into slow and fast components, occur ubiquitously in models of physical, biological and ecological processes. In this talk I will focus on two example applications: the dynamics of vegetation patterns in water-limited regions and the propagation of impulses along nerve fibers. These processes can be modeled by reaction diffusion PDEs in which the patterns arise as traveling wave solutions. The slow/fast timescale separation induces a geometry on the underlying equations which can be exploited to gain insight into the structure and stability of these patterns.

 

Michael Cranston is inviting you to a scheduled Zoom meeting.

Topic: Carter Colloquium
Time: Oct 9, 2020 03:30 PM Pacific Time (US and Canada)

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Invariant theory meets P vs NP

Speaker: 

Visu Makam

Institution: 

Princeton University

Time: 

Friday, January 31, 2020 - 4:00pm to 4:50pm

The study of symmetries in the setting of group actions via “invariant” polynomials is called invariant theory. Throughout the 20th century, invariant theory has had a profound influence in several fields in mathematics, most notably those that fall under the broad purview of algebra. Over the last two decades, new directions in invariant theory have emerged out of connections to computational complexity. Particularly exciting is the Geometric Complexity Theory (GCT) program that has uncovered connections between invariant theory and foundational problems in complexity such as identity testing and the celebrated P vs NP problem.

In this talk, I will discuss recent advances in invariant theory concerning matrix invariants and semi-invariants, (non-commutative) identity testing, null cones and orbit closures. Towards the end, I will discuss some very promising directions for the future in this rapidly expanding field. Based on several joint works with Harm Derksen, Ankit Garg, Rafael Oliveira, and Avi Wigderson.

The Birch and Swinnerton-Dyer Conjecture, one prime at a time

Speaker: 

Florian Sprung

Institution: 

Arizona State University

Time: 

Wednesday, January 29, 2020 - 4:00pm to 4:50pm

Location: 

RH 306

Elliptic curves are simple-looking polynomial equations in two variables whose solutions are still a mystery. The Birch and Swinnerton-Dyer Conjecture (a millennium problem) relates these solutions to a complex function. The conjecture is deep because it connects algebra with analysis. After explaining the conjecture, we discuss some recent results towards it, along with strategies of proving it one prime at a time.

Unraveling local cohomology

Speaker: 

Emily Witt

Institution: 

University of Kansas

Time: 

Monday, January 27, 2020 - 3:00pm to 3:50pm

Location: 

RH 306

Local cohomology modules are fundamental tools in commutative algebra, due to the algebraic and geometric information they carry. For instance, they can help determine the number of equations necessary to define an affine variety. Unfortunately, however, the application of local cohomology is limited by the fact that these modules are typically very large (e.g., not finitely generated), and can be difficult to determine explicitly. In this talk, we discuss new techniques developed to understand the structure of local cohomology (e.g., coming from invariant theory).  We also describe recently- discovered "connectedness properties" of spectra that local cohomology encodes.

Moments in families of L-functions

Speaker: 

Alexandra Florea

Institution: 

Columbia University

Time: 

Friday, January 24, 2020 - 3:00pm to 3:50pm

Location: 

RH 306

The moments of the Riemann zeta function were introduced by Hardy and Littlewood more than 100 years ago, in an attempt to prove the Lindelöf hypothesis, which provides a strong upper bound on the size of the Riemann zeta function on the critical line. Since then, moments became central objects of study in number theory. I will give an overview of the problem of computing moments in different families of L-functions, and I will discuss some of the applications. For example, I will explain how one can extract information about the values of L-functions at special points by computing moments of the L-functions in question.

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