Event(s) on November 2007

• 13/11/2007

  題目:	Stability of Random Networks
  講員:	Prof. Fuzhou Gong, Institute of Applied Mathematics, AMSS, Chinese Academy of Sciences, China
  時間/地點:	11:30  -  12:30 FSC 1217
  摘要:	Recently, there has been considerable interest in studying scale free random network. Although the study of real-world networks as graphs goes back some time, recent activity perhaps was started with the paper of Watts and Strogatz about the "small world phenomenon". Specially, Barabási and Albert proposed a scale-free model and suggested that many real world networks have a power law degree distribution, which is different from the classical random graph introduced by Erdos-Renyi and Gilbert. Since then, the main focus of attention has shifted to the ‘scale-free’ nature of the random networks. Many scientists in different fields have done many different works in the topic, and so many new models and their analysis have been provided. Some works come with empirical and simulative results, while there are only a few mathematical models to describe the scale free random networks. In this talk, firstly we will introduce some nations and notations in random networks. Secondary, we will propose a mathematical model to describe the sale-free networks for Barabási-Albert models. The model can be looked as a graph valued Markov Chain. We proved that there is a stationary power law degree distribution independent on their initial conditions. Moreover, we noticed the stationary degree distribution is only depended on the marginal distributions and the boundary conditions in the random networks. We found that our models have the high clustering coefficients. Finally, we found that the 2-dimension joint distribution had much affect on the clustering coefficients of Barabási-Albert type random networks, and proposed the definition of correlation of Barabási-Albert type random networks. We proved that, it has the high clustering coefficient if the network is positive correlative. We also gave some discussion of the network which is negative correlative.

  
  

• 20/11/2007

  題目:	Estimation of Quantitative Hemodynamic Parameters in MR Perfusion by Using Mathematical Deconvolution Techniques
  講員:	Mr. Chi Pan Tam, Department of Mathematics, Hong Kong Baptist University, Hong Kong
  時間/地點:	14:30  -  15:30 FSC 1217
  摘要:	In bolus-tracking perfusion-weighted MRI, cerebral blood flow (CBF) estimation based on deconvolution techniques. Standard deconvolution problem is modeled from concentration time curve and then solved the integral equation by regularization methods, such as singular value decomposition methods (SVD) and Fourier Transforms (FT). However, most of them are suffered from delay effects. In order to eliminate delay effects, delay insensitive methods and delay correction methods have been proposed. Although both approaches are promising, they are suffering from different kinds of errors. We would like to review the common problems of these approaches in deconvolution process and provide several improvements.