My research operates at the intersection of statistical physics,
computer science, and nonlinear dynamics and has applications to
interdisciplinary problems in social, biological, and technological
systems. Namely, my work falls within the fields of complex networks
and sociophysics. Much of the work is theoretical, but I have been
increasingly interested in using empirical data and sociological experiments to
inform and validate mathematical models.Below is a description of
several projects that I'm currently working on and/or interested in
pursuing. I've tried to elucidate the connections between these
projects as well as how they fit into my larger research agenda of
developing more comprehensive and cohesive approaches within and
between the fields of complex networks and sociophysics.
COMPLEX NETWORKS
Realizing that many complex systems cannot be well
understood without explicitly taking into account how their components are
connected can give us new insights into hard problems. My research addresses
interdisciplinary, network-related problems by tackling broad theoretical
issues, like the optimal deconstruction of complex networks and the detection
of communities in overlapping networks, and then applying these insights toward
the understanding of problems like social network construction, contagion
processes, norm formation, and community fission.
Broad Theoretical Foundations
- Deconstructing
networks. What is the
appropriate way to make first, second, and higher order approximations to
complex networks? How does
this depend on the question at hand? How do we deal with the non-independence of the statistical measures that the network community has been utilizing?
- Global
vs. local signatures of structural complexity.Many current network statistics focus on local
organizational features. What
are the appropriate statistics to capture global complexity?
- Community
structure in overlapping networks. In the presence of multiple networks (consider, for example,
familial, friendship, and colleague networks) how can we identify the existence of and interactions between
overlapping communities?
- Robustness
in complex networks
- How
does the existence of multiple, overlapping networks contribute to or
detract from a system's robustness?
- How
do specialization and generalization of nodes contribute to system
robustness?
Applications of complex networks
- Social
network construction. What
are the rules by which social networks form?
- Social
contagion. How do
fads/ideas/behaviors spread through populations?
- Combining
network and field effects. How are social cascades affected by the interaction of field
effects like mass media with spread through social networks?
- Social
norms and social networks. How do social norms emerge and
evolve? How do they constrained by
the structure of social networks? How are social networks affected by the existence of societal
norms?
SOCIOPHYSICS
Many of my current and developing research projects described above
fall under the umbrella of sociophysics. Broadly speaking,
sociophysics can be described as the search for fundamental laws and
principles that characterize human behavior and result in collective
social phenomena. Included in this field are topics such as the
dynamics of complex social networks (which is how the above work ties
in here), robustness of social processes, econophysics, the scaling of
social systems, and the evolution of social organization. Each of
these subtopics represents a union of what we call a sociophysics
perspective with approaches from other fields.
So what exactly is sociophysics? Sociophysics brings a physics
perspective to the problem of complex collective
behaviors. Individuals are treated somewhat analogously to particles,
e.g. like atoms in a gas. This allows for the application of
statistical physics methodologies. The result is a coarse graining of
many details of individual interactions in search of universal
principles – i.e. laws of society. Of course, human behavior cannot be
simplified to the extent of atoms in a gas – we likely need to include
elements like adaptation and social connectivity. Identifying the
appropriate elements is part of the challenge of sociophysics.
In addition to my social network interests described above, which
obviously fall into the realm of sociophysics, I'm also interested
in herding behavior in animals – How do local interactions between
individuals lead to complex global patterns?
PAST AND PRESENT COLLABORATORS:
- Mark Newman
- Steve Strogatz
- Simon Levin
- David Krakauer
- Jessica Flack
- Adrian de Froment
- Iain Couzin
- Aaron Clauset
I'm currently looking for students and postdocs who are interested in the types of problems described above and have backgrounds in any the following areas:
- Statistical physics
- Applied mathematics
- Computer science
- Mathematical social sciences
- Mathematical and computational biology
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