generalized statistical complexity measure: recent ap p lications

Generalized Statistical Complexity Measure: recent applications.

Dr. Osvaldo A. RossoDepartamento de Física, Instituto de Ciências Exatas,

Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, Brazil

Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires (UBA), Buenos Aires, Argentina

oarosso@gmail.com

oarosso@fibertel.com.ar

Collaborators

• Alejandra Figliola ( Buenos Aires, Argentina)• Eduardo Serrano (Buenos Aires, Argentina)• Maria Teresa Martín (La Plata, Argentina)• Angel Plastino (La Plata, Argentina)• Hilda Larrondo (Mar del Plata, Argentina)• Laura Carpi (Newcastle, Australia)• Patricia Saco (Newcastle, Australia)• Martín Gómez-Ravetti (Belo Horizonte, Brazil)

Quantifiers

• Normalized Shannon Entropy

• Fisher Information Measure

• MPR – Statistical Complexity

• Missing ordinal patterns

Quantifiers

Probability Distribution

Bandt-Pompe Methodology for PDF

Ordinal patterns in a simple time series. (A) Ordinal patterns at the dimension d = 3. (B) Illustration of the ordinal procedure for d = 3 for sine and white noise time series. (C) Probability distribution of ordinal patterns π.

EL Niño/Southern Oscillation during the Holocene

• We study the dynamics of the Holocene proxy ENSO record corresponding to the Laguna Pallcacocha sedimentary data.

• Specifically, we analyse temporal changes in dynamics over the last 11000 years using Information Theory quantifiers.

• Data: The proxy record was obtained from the analysis of clastic laminae deposition in two 8-m sediment cores retrieved from the Pallcacocha Lake in Ecuador.

Moy et al. “Variability of El Niño Southern Oscillation activity at millennial times during the Holocene epoch”. Nature 420 (2002) 162-165

EL Niño/Southern Oscillation during the Holocene

• Information Theory Quantifiers: H, F, C, missing patterns.

• We computed the evolution of the quantifiers through time using a sliding time window of 1000 data values with a lag of 100 data values between successive windows.

• A sliding window was used to allow for a better localization of changes in the dynamics of ENSO through time (ENSO period 3 to 7 years).

• PDF-Histograms: The N_bins = 100 in the interval [38.06, 243.06] (defined by the minimum and maximum amplitude values of the complete time series).

• PDF-Bandt-Pompe: length of patterns of D=5.

EL Niño/Southern Oscillation during the Holocene

The grey bands correspond to the major periods of Holocene rapid climate change (RCC).

EL Niño/Southern Oscillation during the Holocene

The grey bands correspond to the major periods of Holocene rapid climate change (RCC).

EL Niño/Southern Oscillation during the Holocene

The grey bands correspond to the major periods of Holocene rapid climate change (RCC).

EL Niño/Southern Oscillation during the Holocene

EL Niño/Southern Oscillation during the Holocene

Chaos & Noise

Chaos & Noise

Chaos & Noise

Chaos & Noise

Chaos & Noise

Chaos & Noise

Chaos & Noise

Questions & Suggestions

• Thanks a lot !!!

• Muito obrigado !!!

• Muchas gracias !!!