12,134 research outputs found
A method for inferring hierarchical dynamics in stochastic processes
Complex systems may often be characterized by their hierarchical dynamics. In
this paper do we present a method and an operational algorithm that
automatically infer this property in a broad range of systems; discrete
stochastic processes. The main idea is to systematically explore the set of
projections from the state space of a process to smaller state spaces, and to
determine which of the projections that impose Markovian dynamics on the
coarser level. These projections, which we call Markov projections, then
constitute the hierarchical dynamics of the system. The algorithm operates on
time series or other statistics, so a priori knowledge of the intrinsic
workings of a system is not required in order to determine its hierarchical
dynamics. We illustrate the method by applying it to two simple processes; a
finite state automaton and an iterated map.Comment: 16 pages, 12 figure
Synchronizability determined by coupling strengths and topology on Complex Networks
We investigate in depth the synchronization of coupled oscillators on top of
complex networks with different degrees of heterogeneity within the context of
the Kuramoto model. In a previous paper [Phys. Rev. Lett. 98, 034101 (2007)],
we unveiled how for fixed coupling strengths local patterns of synchronization
emerge differently in homogeneous and heterogeneous complex networks. Here, we
provide more evidence on this phenomenon extending the previous work to
networks that interpolate between homogeneous and heterogeneous topologies. We
also present new details on the path towards synchronization for the evolution
of clustering in the synchronized patterns. Finally, we investigate the
synchronization of networks with modular structure and conclude that, in these
cases, local synchronization is first attained at the most internal level of
organization of modules, progressively evolving to the outer levels as the
coupling constant is increased. The present work introduces new parameters that
are proved to be useful for the characterization of synchronization phenomena
in complex networks.Comment: 11 pages, 10 figures and 1 table. APS forma
Multiple dynamical time-scales in networks with hierarchically nested modular organization
Many natural and engineered complex networks have intricate mesoscopic
organization, e.g., the clustering of the constituent nodes into several
communities or modules. Often, such modularity is manifested at several
different hierarchical levels, where the clusters defined at one level appear
as elementary entities at the next higher level. Using a simple model of a
hierarchical modular network, we show that such a topological structure gives
rise to characteristic time-scale separation between dynamics occurring at
different levels of the hierarchy. This generalizes our earlier result for
simple modular networks, where fast intra-modular and slow inter-modular
processes were clearly distinguished. Investigating the process of
synchronization of oscillators in a hierarchical modular network, we show the
existence of as many distinct time-scales as there are hierarchical levels in
the system. This suggests a possible functional role of such mesoscopic
organization principle in natural systems, viz., in the dynamical separation of
events occurring at different spatial scales.Comment: 10 pages, 4 figure
Delegated causality of complex systems
A notion of delegated causality is introduced here. This subtle kind of causality is dual to interventional causality. Delegated causality elucidates the causal role of dynamical systems at the “edge of chaos”, explicates evident cases of downward causation, and relates emergent phenomena to Gödel’s incompleteness theorem. Apparently rich implications are noticed in biology and Chinese philosophy. The perspective of delegated causality supports cognitive interpretations of self-organization and evolution
Coordinated Robot Navigation via Hierarchical Clustering
We introduce the use of hierarchical clustering for relaxed, deterministic
coordination and control of multiple robots. Traditionally an unsupervised
learning method, hierarchical clustering offers a formalism for identifying and
representing spatially cohesive and segregated robot groups at different
resolutions by relating the continuous space of configurations to the
combinatorial space of trees. We formalize and exploit this relation,
developing computationally effective reactive algorithms for navigating through
the combinatorial space in concert with geometric realizations for a particular
choice of hierarchical clustering method. These constructions yield
computationally effective vector field planners for both hierarchically
invariant as well as transitional navigation in the configuration space. We
apply these methods to the centralized coordination and control of
perfectly sensed and actuated Euclidean spheres in a -dimensional ambient
space (for arbitrary and ). Given a desired configuration supporting a
desired hierarchy, we construct a hybrid controller which is quadratic in
and algebraic in and prove that its execution brings all but a measure zero
set of initial configurations to the desired goal with the guarantee of no
collisions along the way.Comment: 29 pages, 13 figures, 8 tables, extended version of a paper in
preparation for submission to a journa
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