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.
Approaches:Multi-scale methodologies
Hierarchical and Clustering Point Processes and Duration models
Random Graphs and Scalefree Trees
Wavelet based estimation and inference
Multiplicative Cascades and Self-similar
processes
Applications to Complex
Systems include:
Communication Networks:
Inference of internal Network state for high performance and
wireless networking
The best of both worlds: Hierarchical,
yet distributed
approaches for multihop ad hoc
networks
Inferring and Modeling of Internet topology and geometry
Computational Finance and Economic Systems:
micro-structure and high-frequency modeling of financial data
Informed networking for a secure ecnomy (anomaly detection)
Methodologies:
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
