Embed Size (px)
Citation preview
Clustering and spreading of behavior and opinion in social networksLazaros GallosLevich Institute, City College of New York
Hernan A. Makse - Shlomo Havlin
Clustering and spreading of behavior in social networksLazaros GallosLevich Institute, City College of New York
Hernan A. Makse - Shlomo Havlin
Obesity epidemic (?)
BMI and obesity
The Body Mass Index (BMI) is a standard measure of human body fat
BMI>30 is generally accepted as the obesity threshold
Obesity in USA increases with time
What we know on obesity ‘spreading’
1. Genetics2. Peer pressure
(Christakis and Fowler, NEJM, 2007)3. Spatial clustering
Our approach
• The physics of clustering is challenging
• Study obesity as a percolation process
• Use scaling analysis
• More properties
Obesity prevalence in USA
Percolation transition
Time evolution of obesity clusters
County obesity %
Largest clusters
County obesity %
Neighbors influence
(after Christakis, Fowler)
Distance-based correlations
The increase rate is also correlated
Spatial correlations:
Scaling theory of Growth
• Standard theory of Gibrat assumes random
growth
• Scaling concepts introduced by the H.E. Stanley
group
(Stanley, Nature, 1996) for the growth of
companies
• Extended to more properties (e.g. cities)
Growth rate:
𝛽=𝛾2𝑑
Limits
𝛽=𝛾2𝑑
High correlations: No correlations:
b =0, g =0 b =0.5 , g=2 (in 2d)
Spatial correlations (constant in time)
g =0.5Obesity
g =1.0Population
Digestive cancer mortality(Changes with time)
Time evolution of g
Weak correlations
Strong correlations
Phase diagram
Uncorrelated
Random walk
Human activity
Economy
City growth
Population
Mortality
Cancer mortality
Obesity
Diabetes
Inactivity
Lung cancer
g /d11/21/4
Weak
correlationsStrong
correlations
Conclusions
• Strong spatial correlations in obesity spreading
• Obesity clusters grow faster than the population growth
• Scaling analysis quantifies the degree of spatial correlations
• Exponents are related
Three main universality classes based on spatial correlations
