Lectures：June-October，2020，Stony Brook University, USA-Xianfeng Gu，Wuhan University, China-Shuang Miao，Shenzhen Institutes of Advanced Technology-Dong Liang，RICAM Austrian Academy of Sciences, Austria-Mourad Sini

Time:   June 4,   8:30-9:30 AM （Beijing time） Lecture   No. 20200604-01

Lecture   website (zoom): https://us02web.zoom.us/j/89536670985

ID:89536670985Password:   20200604

Speaker

Xianfeng Gu   

Affiliation

Stony Brook University,   USA

Title: A geometric understanding   of deep learning

Abstract: This work introduces an optimal transportation (OT) view of generative adversarial networks (GANs).   Natural datasets have intrinsic patterns, which can be summarized as the   manifold distribution principle: the distribution of a class of data is close   to a low-dimensional manifold. GANs mainly accomplish two tasks: manifold   learning and probability distribution transformation. The latter can be   carried out using the classical OT method. From the OT perspective, the   generator computes the OT map, while the discriminator computes the   Wasserstein distance between the generated data distribution and the real   data distribution; both can be reduced to a convex geometric optimization   process. Furthermore, OT theory discovers the intrinsic collaborative—instead   of competitive—relation between the generator and the discriminator, and the   fundamental reason for mode collapse. We also propose a novel generative   model, which uses an autoencoder (AE) for manifold learning and OT map for   probability distribution transformation. This AE–OT model improves the   theoretical rigor and transparency, as well as the computational stability   and efficiency; in particular, it eliminates the mode collapse. The   experimental results validate our hypothesis, and demonstrate the advantages   of our proposed model.

Short Bio: Dr. Xianfeng Gu got his bachelor from Tsinghua university, PhD   in computer science from Harvard university, supervised by the Fields   medalist, Prof. Shing-Tung Yau. Currently, Dr. Gu is a New York State Empire   Innovation Professor in the Computer Science Department, Stony Brook   university. Dr. Gu's research focuses on applying modern geometry in   engineering and medicine fields. Together with Prof. Shing-Tung Yau, Dr. Gu   and other collaborators have founded an interdisciplinary field:   Computational Conformal Geometry. Dr. Gu has won NSF Career award,   Morningside Gold medal in applied Mathematics.

Time:   June 11,   8:30-9:30 AM （Beijing time）Lecture   No. 20200611-02

Lecture   website (zoom): https://us02web.zoom.us/j/84417517383

ID:84417517383Password:   20200611

Speaker

Shuang Miao

Affiliation

Wuhan University, China

Title: On   the free boundary hard phase fluid in Minkowski space

Abstract: I will discuss a   recent work on the free boundary hard phase fluid model with Minkowski   background. The hard phase model is an idealized model for a   relativistic fluid where the sound speed approaches the speed of   light. This work consists of two results: First, we prove the   well-posedness of this model in Sobolev spaces. Second, we give a rigorous   justification of the non-relativistic limit for this model as the speed of   light approaches infinity. This is joint work with Sohrab Shahshahani and   Sijue Wu.

Short Bio: Shuang Miao is a professor at Wuhan University.   His main research interests lie in the singularity formation for nonlinear   wave equations and long time behavior for free boundary problems in inviscid   fluids.

Time:   June 18,   8:30-9:30 AM （Beijing time）Lecture   No. 20200618-03

Lecture   website (zoom):   https://us02web.zoom.us/j/86901726807

ID:86901726807 Password:   20200618

Speaker

Dong Liang

Affiliation

Shenzhen Institutes of Advanced   Technology,

Chinese Academy of Sciences, China

Title: Fast magnetic resonance   imaging: theory, technique and application

Abstract:   Magnetic resonance imaging (MRI) has become   one of the most important medical revolutions and has played a significant   role in modern medical imaging based diagnosis and therapy. However, the   intrinsic relatively slow data acquisition has limited its applications   largely. Usually, acquiring less data is an important strategy for   accelerating MRI, with the proportional relationship between the number of acquired   data and scanning time. However, less acquisition usually results in aliasing   artifacts in reconstructions. Under this circumstance, image reconstruction   problem becomes an ill-conditioned inverse problem. In this talk, we will provide   an overview of the theory for fast MRI, some techniques we developed and   their applications in accelerating MR imaging.

Short Bio: Dr. Dong Liang is a   Full Professor of Biomedical Engineering at Shenzhen Institutes of Advanced   Technology (SIAT), Chinese Academy of Sciences (CAS). He is the Director of   Research center for Artificial Intelligence in Medicine and Deputy Director   of Research center for Biomedical Imaging, SIAT. Dr. Liang’s research has   focused on high-speed magnetic resonance imaging. He has published over 100   peer-reviewed papers and holds 3 U.S. patents and 30 China patents. His   research has been well funded by state agencies, including NSF of China and The Ministry of   Science and Technology of China, province agencies, and CAS. He received   First prize in the BME award from the Chinese Society of Biomedical   Engineering in 2019.He currently serves   on the Editorial Board of Magnetic Resonance in Medicine and is an Associate   Editor of the IEEE Transactions on Medical Imaging. He is a   senior member of IEEE and is an elected member of IEEE Computational Imaging   Technical Committee.

Time:   June 25,   15:30-16:30（Beijing time）Lecture   No. 20200625-04

Lecture   website (zoom):https://us02web.zoom.us/j/84580522524

ID:84580522524 Password: 20200625

Speaker

Mourad Sini

Affiliation

RICAM Austrian Academy of Sciences,   Austria

Title: Mathematical analysis   of the photo-acoustic imaging modality using dielectric nanoparticles as contrast   agents

Abstract: We   will discuss our recent results on the mathematical analysis of the imaging   modalities using injected highly contrasting small agents as the acoustic   imaging, optical imaging and photo-acoustic imaging.It is known that without using such   contrast agents, these imaging modalities are highly instable. However, using   them shows improvement of the stability of the reconstruction, at least for   benign anomalies, see for instance [1] and [2].

Our goal is to understand and   mathematically quantify these findings by providing reconstruction formulas   linking the corresponding measured data, of each modality, to the desired   parameters of the model.

To show this, we will mainly focus on   the photo-acoustic imaging modality using dielectric nanoparticles as   contrast agents. The main argument in our analysis here is that these   dielectric nanoparticles resonate at certain, computable, frequencies.   Exciting the medium with propagating incident waves at frequencies close to   such resonances creates local spots, around the injected nanoparticles, and   enhance the measured fields. This feature is used to extract the unknown   parameters of the model from the remotely measured data.

We will also discuss the acoustic or   /and the optical imaging modalities using the corresponding contrasting agents   (i.e. bubbles and nanoparticles respectively).Parts of the results presented in this talk   can be found in the preprints [3] and [4].

[1]   S. Qin, C. F. Caskey and K. W. Ferrara. Ultrasound contrast microbubbles in   imaging and therapy: physical principles and engineering. Phys Med Biol.   (2009).

[2].   W. Li and X. Chen, Gold nanoparticles for photoacoustic imaging, Nanomedicine   (Lond.) 10(2), 2015.

[3].   A. Ghandriche and M. Sini. Mathematical Analysis of the Photo-acoustic   imaging modality using resonating dielectric nanoparticles: The 2D TM-model.   arXiv:2003.03162

[4].   A. Dabrowski,A. Ghandriche and M.   Sini, Mathematical analysis of the acoustic imaging modality using bubbles as   contrast agents at nearly resonating frequencies. arXiv:2004.07808

This work is supported by the Austrian   Science Fund (FWF): P 30756-NBL.

Short Bio: Mourad Sini received his PhD   degree from University of Provence, France, in 2002. Then he moved to   Hokkaido University, Japan, where he worked during the two years 2003-2005 as   a postdoc fellow of the Japanese Society for the Promotion of Sciences   (JSPS). He spent the academic year 2005-2006 as a visiting professor at   Yonsei University in Seoul, Korea. Since 2006, he joined the Radon Institute,   RICAM, of the Austrian Academy of Sciences where he is affiliated as a senior   fellow. Mourad Sini is an applied mathematician working in inverse problems,   mathematical imaging and material sciences.