Mathematics Colloquium Schedule

Fall 2019

 

Date: 12-6-2019 (12pm-1pm, F03-200A), Dr. Xiaolong Li, Department of Mathematics, UCSD.

Title: Gradient Ricci Solitons and Their Classifications

Abstract: Gradient Ricci solitons are natural generalization of Einstein manifolds. They may be regarded as self-similar solutions to Hamilton's Ricci flow. As such, they are important in the singularity analysis of Ricci flow. Indeed, the blow-ups around a type-I singularity point always converge to nontrivial gradient shrinking Ricci solitons. It is thus a central issue in the study of Ricci flow to understand the geometry, topology and classification of gradient Ricci solitons. In this talk, I will give a brief introduction to gradient Ricci solitons and then present several classification results under positivity of curvature conditions, based on joint work with Professor Lei Ni.
 

Date: 11-22-2019 (12pm-1pm, F03-200A), Dr. Gary Green, SIAM Visiting Lecture Series, retired from Aerospace Corporation.

Title: Region Coverage from a Satellite … (Insight into Industrial Mathematics)

Abstract: Suppose we have a satellite-based sensor that can see anything within a right circular cone (think of a flashlight beam).  It is a matter of trigonometry and finding the zeros of a function to find when the sensor sees a point on the earth surface and tools to determine such visibilities are in daily use.  Suppose we replace the point with a region (for example, the state of Washington), desiring to know when the sensor sees some portion of the region.  Solving this problem is challenging (and incomplete), yet is within the reach of many undergraduates. Target Audience:  Undergraduates with limited linear algebra and calculus

 

Date: 11-19-2019 (Tuesday, 2pm-3pm, F03-200A), Dr. Dr. Alessandro Corbetta, Eindhoven University of Technology.

Title: Learning turbulence from deep learning

Abstract: Deep neural network (DNN) models are at the center of the present machine learning revolution. The set of complex tasks in which they over perform human capabilities and best algorithmic solutions grows at an impressive rate and includes, but it is not limited to, image, video and language analysis, automated control, and even life science modeling. Besides, deep learning is receiving increasing attention in connection to a vast set of problems in physics where quantitatively accurate outcomes are expected.

In this talk -after a crash introduction to the basic concepts in DNNs- I will discuss our recent investigation of the capabilities of a state-of-the-art deep neural model at learning features of turbulent velocity signals.

We considered Lagrangian turbulent velocity signals spanning decades in Reynolds number, which have been generated via shell models for the turbulent energy cascade. Given the multi-scale nature of turbulent signals, we focus on the fundamental issue of whether a DNN is capable of learning, after supervised training with very high statistics, feature extractors to address and distinguish intermittent and multi-scale signals. The driving questions are: can the DNN measure the Reynolds number of the signals? Which feature is the DNN learning?

We show that the DNN learns complex and entangled multi-scale features which result in estimates of the Reynolds number incredibly more accurate than what achievable via analyses based on Kolmogorov-like scaling arguments. The  performance of the DNN remain stunningly high even when restricted on only few integral eddy turnover times. We thoroughly report on the network performance and feature extractors as a parametric study delivered performance vs. input spectral content.

This work is in collaboration with V. Menkovski (TU Eindhoven), R. Benzi (Tor Vergata, Rome) and F. Toschi (TU Eindhoven).

 

Date: 11-15-2019 (12pm-1pm, F03-200A), Lingjing Jiang, UCSD Biostats PhD program Outreach.

Title: Bayesian Sparse Functional Principal Components Analysis Models Dynamic Temporal Changes in Longitudinal Microbiome Studies

Abstract: Longitudinal microbiome studies provide valuable information about dynamic interactions between the microbiome and host, by capturing both between-individual differences and within-subject dynamics. As the costs of DNA sequencing have decreased, microbiome researchers have a greater opportunity to perform longitudinal studies to better understand microbial changes in response to an intervention in real time. However, microbial communities can change abruptly in response to small perturbations. Current approaches for longitudinal microbiome analysis are not sufficient to capture this dynamic temporal variation, especially with the additional challenges of irregular sampling intervals, limited sample size, missing values and dropouts. We developed a Bayesian Sparse Functional Principal Components Analysis (SFPCA) methodology to meet the growing need to model dynamic temporal change and to detect its dependence on biological covariates in longitudinal microbiome analysis. We show in simulations and in real data applications that Bayesian SFPCA is able to overcome the above challenges in longitudinal microbiome analysis, and is more sensitive for capturing temporal variations and detecting differences due to biological covariates than existing methods. 

At the end of the talk, she will introduce the biostatistics PhD program in UCSD and encourage our students to apply.

 

Date: 11-8-2019 (12pm-1pm, F03-200A), Dr. Shabnam Sodagari, EE Department, CSULB.

Title: Applications of Mathematics in Telecommunications

Abstract: Telecommunication engineering has been interwoven with mathematics since its early inception to date and in the future. In this talk, we address some recent developments that shape upcoming standards, such as 5G and beyond. As illustrative examples, we elaborate on the latest machine learning techniques for efficient use of wireless resources (e.g., in NOMA or non-orthogonal multiple access) that lead to higher speeds and lower delays in next generations of wireless communications to support Internet of Things (IoT). We further investigate possibilities for improving.

 

Date: 11-1-2019 (12pm-1pm, F03-200A), Dr. Yanxiang Zhao, George Washington University.

Title: Energy Stable Semi-Implicit Schemes for Allen-Cahn-Ohta-Kawasaki Model in Binary/Ternary System

Abstract: We propose a first order energy stable linear semi-implicit method for solving the Allen-Cahn-Ohta-Kawasaki equation. By introducing a new nonlinear term in the Ohta- Kawasaki free energy functional, all the system forces in the dynamics are localized near the interfaces which results in the desired hyperbolic tangent profile. In our numerical method, the time discretization is done by some stabilization technique in which some extra nonlocal but linear term is introduced and treated explicitly together with other linear terms, while other nonlinear and nonlocal terms are treated implicitly. The spatial discretization is performed by the Fourier collocation method with FFT-based fast implementations. The energy stabilities are proved for this method in both semi-discretization and full discretization levels. Numerical experiments indicate the force localization and desire hyperbolic tangent profile due to the new nonlinear term. We test the first order temporal convergence rate of the proposed scheme. We also present hexagonal bubble assembly as one type of equilibrium for the Ohta-Kawasaki model. Additionally, the two-third law between the number of bubbles and the strength of long-range interaction is verified which agrees with the theoretical studies.

 

Date: 10-25-2019 (12pm-1pm, F03-200A), Dr. Yunied Puig de Dios, UC Riverside.

Title: On the interplay of functional analysis and operator theory

Abstract: We overview some basic and striking facts concerning the theory of hypercyclic operators (considered to be born in 1982):

  1. Hypercyclicity is a purely infinite-dimensional phenomenon: no finite dimensional space supports any hypercyclic operator;
  2. It is not easy at all to determine whether a linear operator is hypercyclic. However, the set of hypercyclic operators is dense for the Strong Operator Topology in the algebra of linear and bounded operators;
  3. Hypercyclicity is far from being an exotic phenomenon: any infinite-dimensional separable Frechet space supports a hypercyclic operator.
     

Date: 10-11-2019 (12pm-1pm, F03-200A), Professor Janet Duncan, UC Santa Barbara.

Title: Property/Casualty Insurance Loss Reserving Methods

Abstract: There are three fundamental methods that property/casualty actuaries utilize in estimating ultimate losses and reserves: Expected Method, Development Method, Bornhuetter-Ferguson Method. The advantage of these methods is how simple they are. In fact, all three methods pre-date computers but are still widely used and accepted because they produce reasonable results (in most cases) and are simple to explain. These days, software is used to perform the calculations. However, there is room for improvement.
 

Date: 10-04-2019 (12pm-1pm, F03-200A), Dr. Qixuan Wang, UC Riverside.

Title: Impacts of Cellular Heterogeneity on Hair Follicle Growth Dynamics

Abstract: Hair follicle is a mini-organ in mammalian skin that can undergo cyclic growth, whose spatial and temporal dynamics are under tight regulatory control mechanisms from both intra- and extra-follicular environment. Recent experimental results have elucidated how certain signaling pathways regulate cell divisions, differentiation and programmatic death in different parts of the follicle. However, an integrated regulatory mechanism of hair follicle growth dynamics is still unclear at present. In particular, two crucial questions stay unresolved: 1) how does the hair follicle know if it has reached the maximum length, and 2) how does the hair follicle know when to terminate anagen and enters catagen? Using a novel multi-scale model, we discover how a cooperative signaling network regulates the cell lineage dynamics during anagen and early catagen. Preliminary modeling results indicate that cellular heterogeneity in response to signals play an important role in controlling the hair follicle growth dynamics. In particular, we find that heterogeneity in the responses of outer root sheath cells to proliferation vs. differentiation signals determines the hair follicle length. Next, heterogeneity in the responses of matrix cells to proliferation vs. differentiation signals allows longer anagen by enhancing cell competitions. Moreover, the heterogeneous response of matrix cells to the signals allows great anagen duration variability subjected to Bmp level changes.

 

Date: 09-27-2019 (11am-12pm, F03-200A), Dr. Jiajia Dong, Bucknell University.

Title: Modeling Colony Pattern Formation under Differential Adhesion and Cell Proliferation

Abstract: Proliferation of individual cells is one of the hallmarks of living systems, and collectively the cells within a colony or tissue form highly structured patterns, influencing the properties at the population level. We develop a cellular automaton model that characterizes bacterial colony patterns emerging from the joint effect of cell proliferation and cell-cell differential adhesion. Through simulations and theoretical analysis akin to interface growth, we show that this model gives rise to novel properties consistent with recent experimental findings. We observe slower than exponential growth in the case of a single cell type as well as new colony patterns in the case of two cell types. In particular, engulfment of one cell type by the other is strongly enhanced compared to the prediction from the equilibrium differential adhesion hypothesis in the absence of proliferation. These observations provide new insights in predicting and characterizing colony morphology using experimentally accessible information such as single cell growth rate and cell adhesion strength.