Multiscale Statistics for Evolving Complex Systems

My research focuses on the development of multiscale methodologies, for modeling, estimation and inference, as well as simulation, emphasizing on applications to complex systems with evolutionary components. Applied areas include primarily the study of networks as diverse as the internet and financial systems with particular interest in activity profiles, topologies and geometries, as well as anomaly detection and measures of risk. Secondary interests include turbulent flows, medical data and geophysics.

The statistical setting of my work embraces both, non-parametric and parametric estimation and builds on wavelets, clustering, point regression and related techniques. The stochastic models I devised leverage both, linear as well as non-linear and non-stationary (evolutionary) formulations. Research tools combine measurement, simulation and analysis.

Spatio-temporal probing scheme
Scaling plot
Infinitely Divisible Cascade (Noise)
Inference of Workload through
finite population sampling and probing
Wavelet based inference
of Heavy tails
Simulation of complex time series

Model of Lung captures developmental differences in adult, newborn and fetal lung via its multiscale/hierarchical structure
Lung Model
Human Lung
Actual Lung
click for animation of scaling analysis