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Networks composed of vertices (or nodes) and edges (or links)
provide a general framework for the representation
of many different systems. First,
any system with a discrete state space can be viewed
as a network, in which the vertices represent the different states of the system
and the edges correspond to possible transitions between these states.
One example is provided by
network representations of
molecular motors.
[1]
[2]
Second, composite systems that consist of
many different but similiar components can also be viewed as networks,
in which the vertices represent the different components and the edges correspond to
"interactions" between these components.
In general, the different components of the system can attain several internal
states that evolve with time. The simplest case is provided by binary variables that
can be active or inactive.
[3]
[4]
At any given time, the state of the composite system is then characterized by an
activity pattern of the network, and the system's dynamics is described by the
time evolution of this pattern. Depending on the inital pattern, the system will reach one
of the dynamical attractors that govern the system's long-time behavior.
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J. Menche, A. Valleriani, and R. Lipowsky
Sequences of phase transitions in Ising models on correlated networks.
Phys. Rev. E 83, 061129 (2011).
-
V. Bierbaum and R. Lipowsky
Chemomechanical coupling and motor cycles of myosin V.
Biophys. J. 100, 1747-1755 (2011).
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J. Menche, A. Valleriani, and R. Lipowsky
Asymptotic properties of degree-correlated scale-free networks.
Phys. Rev. E 81, 046103 (2010).
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S. Liepelt and R. Lipowsky
Impact of slip cycles on the operation modes and efficiency
of molecular motors.
J. Stat. Phys. 141, 1-16 (2010).
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J. Menche, A. Valleriani, and R. Lipowsky
Dynamical processes on dissortative scale-free networks.
EPL 89, 18002 (2010).
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R. Lipowsky, S. Liepelt, and A. Valleriani
Energy conversion by molecular motors coupled to
nucleotide hydrolysis.
J. Stat. Phys. 135, 951-975 (2009).
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S. Liepelt and R. Lipowsky
Kinesin's network of chemomechanical motor cycles.
Kinesin's network of chemomechanical motor cycles - Appendices.
Phys. Rev. Lett. 98, 258102 (2007).
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S. Liepelt and R. Lipowsky
Steady-state balance conditions for molecular motor cycles and stochastic nonequilibrium
processes.
EPL 77, 50002 (2007).
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H. Zhou and R. Lipowsky
Activity patterns on random scale-free networks: global dynamics arising from local majority
rules.
J. Stat. Mech. - Theo. & Exp. P01009 (2007).
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H. Zhou and R. Lipowsky
Dynamic pattern evolution on scale-free networks.
Dynamic pattern evolution on scale-free networks - Supporting Information.
PNAS 102, 10052 - 10057 (2005).
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H. Zhou and R. Lipowsky
Network Brownian Motion: A New Method to Measure Vertex-Vertex
Proximity and to Identify Communities and Subcommunities.
Lecture
Notes Comp. Science 3038, 1062-1069 (2004).
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R. Lipowsky and S. Klumpp
'Life is Motion': Multiscale motility of molecular motors.
Physica A 352, 53-112, (2005).
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R. Lipowsky.
Universal aspects of the chemo-mechanical coupling for molecular
motors.
Phys. Rev. Lett. 85 , 4401-4404 (2000).
