Abstract: Spatio-temporal patterns are common in a complex system as in our brain. How to first reveal these patterns, explore their functional meaning and finally model them is an interesting issue in applied mathematics/statistics. In the talk, we will first look for short time window patterns in mins for cognitive tasks and then long time window patterns in days, months and years for brain diseases. Short time window patterns such as sink, source and vortex are closely related to reaction time and information processing in the brain. Long time window patterns help us seek the roots of various brain diseases including depression, schizophrenia and OCD etc. Next we aim for developing a digital twin model (DTB) for simulating the whole human brain with 86B neurons and 100T parameters, the conductance of AMPA, NMDA, GABAA and GABAB. By developing novel methods on routing and data assimilation, DTB has a correlation coefficient above 0.9 with its biological counterpart. In a visual and aural task, the correlation coefficient between DTB and biological counterpart is around 0.6. Finally possible applications of DTB are included.