Phil 3.22.2022

Unveiling the higher-order organization of multivariate time series

  • Time series analysis has proven to be a powerful method to characterize several phenomena in biological, neural and socio-economic systems, and to understand their underlying dynamical features. Despite a plethora of methods having been proposed for the analysis of multivariate time series, most of them do not investigate whether signals result from independent, pairwise, or group interactions. Here, we propose a novel framework to characterize the temporal evolution of higher-order dependencies within multivariate time series. Using network analysis and topology, we show that, unlike traditional tools, our framework robustly differentiates various spatiotemporal regimes of coupled chaotic maps, including chaotic dynamical phases and various types of synchronization. By analysing fMRI signals, we find that, during rest, the human brain mainly oscillates between chaotic and few partially intermittent states, with higher-order structures reflecting sensorimotor areas. Similarly, in financial and epidemic time series, instead, higher-order information efficiently discriminates between radically different coordination and spreading regimes. Overall, our approach sheds new light on the higher-order organization of multivariate time series, allowing for a better characterization of dynamical group dependencies inherent to real-world systems.


  • 8:30 Meeting
  • 9:15 standup + went over generator concept
  • 2:00 meeting with Ron
  • Need to set up overleaf project and add meeting notes section – in progress
  • Continue on code generator
  • Here’s my fancy piece of code for the dat that sets attributes from a dict:
class HierarchyModule:
quantity: int
name: str
parent: str

def __init__(self, d:Dict):
self.quantity = 1 #default

def to_string(self) -> str:
return "name = {}\n\tquantity = {}\n\tparent = {}\n\tcommands = {}".format(, self.quantity, self.parent, self.commands)
  • Pretty pleased with how this is going: