报告题目：Dual-Value Functions of Dual Matrices with Applications in Causal Emergence

报告人：丁维洋 研究员

报告人单位：复旦大学数学科学学院

报告时间：2024年11月26日上午10:00-11:00

会议地点：数学科学学院301

主办单位：曲阜师范大学数学科学学院

报告摘要：We propose a novel approach to extending the real-valued functions of matrices to the dual-valued functions of dual matrices, with a foundation of the Gateaux derivative. Theoretically, the general forms of dual vector norms and dual matrix norms, remaining the properties in the real field, are provided. In particular, we focus on the dual vector p-norm and the dual matrix Ky Fan p-k-norm. The equivalence between the dual matrix Ky Fan p-k-norm and the dual vector p-norm of the first k singular values of the dual matrix under certain conditions is then demonstrated. Practically, we define the dual transitional probability matrix (DTPM), as well as its effective information (EI). Additionally, we elucidate the correlation between the EI of a DTPM, its dual matrix Ky Fan p-k-norm, and the proximity of the DTPM being dynamically reversible. Through numerical experiments of simulated time-series data, we explore how parameters (k, p) of the dual matrix Ky Fan p-k-norm affect the causal emergence of the system. Finally, this finding is employed in the context of large-scale brain fMRI data to identify the optimal number of classification categories and further substantiate the alignment between the analytical results and the extant knowledge on the division of the cerebral cortex.

报告人简介：

丁维洋研究员现在就职于复旦大学类脑智能科学与技术研究院，于2011年和2016年在复旦大学数学科学学院获得数学与应用数学专业的学士学位和计算数学专业的博士学位，其后在香港理工大学应用数学系作博士后研究，2017至2020年在香港浸会大学数学系担任研究助理教授。于2020年11月加入复旦大学类脑智能科学与技术研究院。丁研究员近期的主要研究兴趣包括张量计算和优化及其在脑与类脑科学中的应用，他出版了1本学术专著，发表了18篇期刊和会议论文，其中有3篇是ESI高被引论文，1篇获得中国计算数学学会优秀青年论文二等奖。他主持1项国家自然科学基金委的青年科学基金项目，1项上海脑科学与类脑研究中心“求索杰出青年”计划项目，1项上海市“科技创新行动计划”自然科学基金项目和1项国家自然科学基金委面上项目。2024年获得上海市自然科学二等奖。