Event(s) on December 2022

• Wednesday, 7th December, 2022

  Title:	Step-size Independent Theoretical Bounds for Preconditioning Techniques
  Speaker:	Dr Xuelei Lin, Harbin Institute of Technology (Shenzhen)
  Time/Place:	16:00  -  17:00 Zoom, Meeting ID: 910 6258 3121
  Abstract:	It is well-known that the condition number of coefficient matrices arising from discretization of differential equations increases as the grid gets refined, because of which iterative solvers converges slowly for the linear systems when the grid is dense. In this talk, preconditioning techniques for dicretization of some differential equations are introduced, with which some Krylov subspace solvers for the preconditioned systems are proven to have a linear convergence rate independent of the stepsizes. Numerical results are also reported.

  
  

• Tuesday, 13th December, 2022

  Title:	An integrated approach for analyzing spatial transcriptomic data by leveraging single-cell data
  Speaker:	Dr. Xiang Wan, Shenzhen Research Institute of Big Data, Shenzhen, China
  Time/Place:	14:30  -  15:30 FSC1217
  Abstract:	Single-cell RNA sequencing (scRNA-seq) characterizes the whole transcriptome of individual cells within a given organ but it does not capture the spatial distribution of cells. As spatial information is so critical to understand communication between cells, many scientific questions related to cellular communication cannot be fully addressed by scRNA-seq alone. To study the spatial distribution of gene expression, many spatial transcriptomics (ST) technologies have been developed to quantify spatially localized transcriptomes, which accelerated the capacity to elucidate the development of healthy tissue and tumor microenvironment of cancers. In this talk, I will introduce our recent ongoing work, a unified framework to combine the scRNA-seq data with various forms of spatial data collected from the same tissue. Our method addresses two challenges in spatial transcriptomics: single-cell resolution cell type identification and single-cell resolved high-throughput transcriptome inference.

  
  

• Tuesday, 13th December, 2022

  Title:	Semiparametric Efficient G-estimation with Invalid Instrumental Variables
  Speaker:	Dr. Zhonghua Liu, Department of Biostatistics, Columbia University, New York, USA
  Time/Place:	15:30  -  16:30 FSC1217
  Abstract:	The instrumental variable method is widely used in the health and social sciences for identification and estimation of causal effects in the presence of potential unmeasured confounding. In order to improve efficiency, multiple instruments are routinely used, leading to concerns about bias due to possible violation of the instrumental variable assumptions. To address this concern, we introduce a new class of g-estimators that are guaranteed to remain consistent and asymptotically normal for the causal effect of interest provided that a set of at least $gamma$ out of $K$ candidate instruments are valid, for $gammaleq K$ set by the analyst ex ante, without necessarily knowing the identity of the valid and invalid IVs. We provide formal semiparametric efficiency theory supporting our results. Both simulation studies and applications to the UK Biobank data demonstrate the superior empirical performance of our estimators compared to competing methods.

  
  

• Wednesday, 14th December, 2022

  Title:	Energy Based Mathematical Modeling, Simulation, and Control of Multi-physics Systems
  Speaker:	Prof Volker Mehrmann, Department of Mathematics, TU Berlin, Germany
  Time/Place:	16:00  -  17:00 Zoom, (Meeting ID: 914 7204 1352)
  Abstract:	Most real world dynamical systems consist of subsystems from different physical domains, modelled by partial-differential equations, ordinary differential equations, and algebraic equations, combined with input and output connections. To deal with such complex system, in recent years the class of dissipative port-Hamiltonian (pH) descriptor systems has emerged as a very successful modeling methodology. The main reasons are that the network based interconnection of pH systems is again pH, Galerkin projection in PDE discretization and model reduction preserve the pH structure and the physical properties are encoded in the geometric properties of the flow as well as the algebraic properties of the equations. Furthermore, dissipative pH system form a very robust representation under structured perturbations and directly indicate Lyapunov functions for stability analysis. Another advantage of energy based modeling via pH systems is that each separate model of a physical system can be a whole model catalog from which models can be chosen in an adaptive way within simulation and optimization methods. We discuss the class of pH descriptor systems and illustrate how many classical real world mathematical models can be formulated in this class. We illustrate the results with some real world examples from gas transport and district heating systems and point out emerging mathematical challenges.

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