Symposium| Institute of Mathematical Sciences
Organizer： Shixiao Jiang
Date：Thursday, June 24th
Mathematical modeling and scientific computing play an important role in applied mathematics and modern sciences. With the development of computers and data sciences, good mathematical models and efficient numerical algorithms have shown the powerful applications in solving many difficult and challenging scientific and engineering problems. The series of IMS (Institute of Mathematical Sciences) CCAM aim to bring together excellent young researchers inside China to share their modern thoughts and state of the art researches in the field of computational and applied mathematics. The colloquium will cover various of topics of applied mathematics, including machine learning, fluid dynamics, material sciences, computational neural sciences, image processing, computational physics and biology, etc. Welcome for your attendance.
Title: Adaptive Acceleration for First-order Methods
Speaker: Jingwei Liang, Queen Mary University of London
Abstract: First-order operator splitting methods are ubiquitous among many fields through science and engineering, such as inverse problems, image processing,statistics, data science and machine learning, to name a few. In this talk, through the fixed-point sequence, I will first discuss a geometry property of first-order methods when applying to solve non-smooth optimization problems. Then I will discuss the limitation of current widely used inertial acceleration technique, and propose a trajectory following adaptive acceleration algorithm. Global convergence is established for the proposed acceleration scheme based on the perturbation of fixed-point iteration. Locally, connections between the acceleration scheme and the well studied vector extrapolation technique in the field of numerical analysis will be discussed, followed by acceleration guarantees of the proposed acceleration scheme. Numeric experiments on various first-order methods are provided to demonstrate the advantage of the proposed adaptive acceleration scheme.
Title: Mathematical Modeling and Analysis of Single-neuron Dendritic Computation
Speaker: Songting Li, Shanghai Jiao Tong University
Abstract: Dendrites are very important for neuronal information processing in the brain. Due to the complex spatial structure and nonlinear ion channels of the dendrites, mathematical theories to quantify the computation of dendrites are still lacking. In this talk, we will first construct the nonlinear PDE cable model, and then convert the nonlinear system to a hierarchy of linear PDE models using asymptotic analysis. By solving the hierarchical system, we can obtain a bilinear rule that charactierzes the integration of multiple input signals received on the dendrites of a neuron. Furthermore, We will derive a simplified ODE model describing the voltage dynamics of a real neuron's soma via model reduction analysis. Our theory and new model have been successfully verified in experiments, which provides an efficient framework for the design of fast numerical simulation algorithms and also provides new thoughts on the design of brain-inspired machine learning algorithms.
Title: A Spectral Immersed Boundary Method for Particles in a Stokes Flow
Speaker: Zecheng Gan , The Hong Kong University of Science and Technology in Guangzhou
Abstract: In this talk, I will introduce a spectral immersed boundary method for particle suspensions in Stokes flow on doubly periodic domains.
Title: Elastic Net and Cortical Map Learning
Speaker: Wei Dai, Courant Institute of Mathematical Sciences - NYU
Abstract: In this talk, I will introduce the elastic net algorithm, properties of the cortical map of visual cortex, and the application of the algorithm in constructing such a cortical map. Finally, I would like to explore the possible correspondence between cortical map learning vs. the elastic net.