Speaker: Dr. Linquan Bai (Department of Systems Engineering & Engineering Management, UNC Charlotte)

Date/Time/Place: 2:00–3:00pm, March 27 (Friday), Fretwell 315.

Title: Transition to Risk Driven Power Grid Operation and Management

Abstract: Affordable and reliable electricity is fundamental to society. Today’s power grid is facing more risks than ever from uncertain renewable power generation, more frequent severe weather events, and cyber-attacks. Integrating emerging technologies such as renewable energy, energy storage, and electric vehicles, the management system of the power grid should evolve to a risk-driven paradigm to effectively manage, hedge and mitigate the system risks. The transition of the power grid management system necessitate advanced risk-theory to analyze probability and uncertainty quantification of renewable generation and vulnerability in power grid topology, optimization approaches for risk-averse optimal power grid scheduling, machine learning for cyberattack detection, etc. I will present the challenges today’s power grid is facing and applications of these new theories and methodologies in addressing the challenges.

Conference room, 11:00 am-12:00 pm

Dr. Tien-Khai Nguyen, NC State University.

Title: Differential Game Models of Optimal Debt Management 
Abstract: In this talk, I will present recent results on game theoretical formulation of optimal debt management problems in infinite time horizon with exponential discount, modeled as a noncooperative interaction between a borrower and a pool of risk-neutral lenders. Here, the yearly income of the borrower is governed by a stochastic process and bankruptcy instantly occurs when the debt-to-income ratio reaches a threshold. Since the borrower may go bankrupt in finite time, the risk-neutral lenders will charge a higher interest rate in order to compensate for this possible loss of their investment. Thus, a “solution” must be understood as a Nash equilibrium, where the strategy implemented by the borrower represents the best reply to the strategy adopted by the lenders, and conversely. This leads to highly nonstandard optimization processes.

Date: February 21, 2020

Time and location:  11:10am-12:10pm, Fretwell 305

Speaker:  Mingyao Li, Ph.D, Department of Biostatistics, Epidemiology & Informatics, University of Pennsylvania Perelman School of Medicine

Title:   Translation of single-cell genomics into human health: methods and applications

Abstract:   Recent technological breakthroughs have made it possible to measure gene expression at the single-cell level, thus allowing biologists and clinicians to better understand cellular heterogeneity and modify cell behavior through targeted molecular therapies. However, single-cell RNA sequencing protocols are complex. Even with the most sensitive platforms, the data are often noisy owing to a high frequency of dropout events, and the phenomenon of transcriptional bursting in which pulses of transcriptional activity are followed by inactive refractory periods. In this talk, I will present several statistical and machine learning methods that aim to tackle these challenges for a better understanding of cellular heterogeneity. I will illustrate our methods by showing results from ongoing collaborations on age-related macular degeneration and Alzheimer’s disease. With the growing interest in utilizing single-cell RNA sequencing in biomedical research, our methods will aid biomedical researchers to answer medically related questions and make exciting discoveries.

Dr. Thi-Phong Nguyen, University of Minnesota (hosted by Loc Nguyen)

Title: Sampling methods for inverse elastic scattering problems in finite solid bodies. 
Abstract: I will present and discuss in this talk sampling methods to reconstruct partially-closed fractures in rock from surface seismic measurements. For the mathematical viewpoint, the fracture is characterized by a second order tensor synthesizing its special stiffness – relation the jump in seismic field cross the fracture to the contact traction. This method relies on a careful analysis of so-called Generalized Linear Sampling Method to build an indicator function for detecting the fracture. The first challenging of this problem is tensorial quantity intrinsically dependent on the fractures’ aperture and the surface roughness, which makes it partially heterogeneous and difficult to solve. The second one is to deal with the near-filed measurement (which has very little reference) and to numerically approximate the gradient of Green tensor in finite space, which can not be expressed by an analytic formula. Some related numerical results will be presented at the end. 

Speaker: Dr. Lu Lu from Brown University (hosted by Xingjie Li).

Title: Learning dynamical systems and differential equations with deep learning: physics-informed and data-driven
Abstract: Deep learning has achieved remarkable success in diverse applications; however, its use in learning dynamical systems and partial differential equations (PDEs) has emerged only recently. These learning approaches can be either physics-informed or data-driven. In the physics-informed approach, I have improved the physics-informed neural networks (PINNs) and developed the library DeepXDE for solving different types of PDEs, including integro-differential equations, fractional PDEs, and stochastic PDEs. In the data-driven approach, I have developed the deep operator network (DeepONet) based on the universal approximation theorem of operators to learn dynamical systems accurately and efficiently from a relatively small dataset. In addition, I will present my work on the deep learning theory of optimization and generalization, and the application of applying multi-fidelity neural networks to predict mechanical properties of solid materials.

Dr. Ling Xu from North Carolina Agricultural and Technical State University (hosted by Professor Xingjie Li).

Title: Vortex dynamics computed by Lagrangian methods

Abstract: The work is built upon the research on two-dimensional inviscid fluid dynamics like the merger, filamentation, instability using magnetized electron columns in the laboratory (Durkin & Fajans, PRL, 2000). These fundamental fluid dynamics phenomena find applications in hurricanes, turbulence, and oceanography. In the work, we are using two numerical methods, particle-panel vortex method and contour dynamics, to study the vortex filamentation and mergers. Techniques such as adaptive-point-insertions and tree-code are employed to increase the accuracy and speed up the simulations. In the end, I will talk about an on-going project on studying material transport using Machine Learning.

Prof. Kevin Lee, Western Michigan University (Hosted by Jun Song)

Title:   Clustering Time-Evolving Networks through Temporal ERGMs

Abstract: Model-based clustering of dynamic networks has emerged as one of the increasingly important research topics in statistical network analysis. We present a statistical clustering framework through the temporal exponential-family random graph models (ERGMs). The temporal ERGMs allow the specification of interesting network features (e.g., stability), and the hidden Markov structure allows the inference of the dynamic latent block structure. In this talk, we will introduce two models one with static latent block structure and the other with dynamic latent block structure. Furthermore, we will discuss a variational expectation-maximization algorithm to solve the approximate maximum likelihood estimation. The performance of our proposed methods is demonstrated through an empirical application to the international trade networks.

Professor Ion Grama, Universite  Bretagne Sud, Lorient (UBS)

Title: Conditioned limit theorems for products of random matrices and Markov chains with applications to branching processes.

Abstract: Consider a random walk defined by the consecutive action of independent identically distributed random matrices on a starting point outside the unit ball in the d dimensional Euclidean space. We study the first moment when the walk enters the unit ball. We study the exact behaviour of this time and prove conditioned limit theorems for the associated Markov walk. This extends to the case of walks on group GL(d,R) the well known results by Spitzer. The existence of the harmonic function related to the Markov walk turns out to be crucial point of the proof. We have extended these results to general Markov chains and applied them to study the branching processes in Markov environment.    

Speaker: Prof. Zhezhen Jin, Columbia University (Hosted by Jiancheng Jiang)

Title:   Variance estimation in semiparametric regression models

Abstract: In semiparametric regression analysis, objective functions and estimating functions for regression parameters are often nonsmooth and non-monotone, which results in difficulty in the corresponding variance estimation. I will discuss the issues and present available and newly developed  methods with general theory, implementation and demonstrate the methods with examples.

Prof. Yanqing Wang, Georgia State University (Hosted by Yinghao Pan)

Title:   Learning-Based Biomarker-Assisted Rules for Optimized Clinical Benefit under A Risk-Constraint

Abstract: Novel biomarkers, in combination with currently available clinical information, have been sought to improve clinical decision making in many branches of medicine, including screening, surveillance, and prognosis. Statistical methods are needed to integrate such diverse information to develop targeted interventions that balance benefit and harm. In the specific setting of disease detection, we propose novel approaches to construct a multiple-marker-based decision rule by directly optimizing a benefit function, while controlling harm at a maximally tolerable level. The new approaches include plug-in and direct-optimization-based algorithms, and they allow for the construction of both nonparametric and parametric rules. A study of asymptotic properties of the proposed estimators is provided. Simulation results demonstrate good clinical utilities for the resulting decision rules under various scenarios. The methods are applied to a biomarker study in prostate cancer surveillance.