27,867 research outputs found
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
A semantic-based platform for the digital analysis of architectural heritage
This essay focuses on the fields of architectural documentation and digital representation. We present a research paper concerning the development of an information system at the scale of architecture, taking into account the relationships that can be established between the representation of buildings (shape, dimension, state of conservation, hypothetical restitution) and heterogeneous information about various fields (such as the technical, the documentary or still the historical one). The proposed approach aims to organize multiple representations (and associated information) around a semantic description model with the goal of defining a system for the multi-field analysis of buildings
Hyperbolic Geometry of Complex Networks
We develop a geometric framework to study the structure and function of
complex networks. We assume that hyperbolic geometry underlies these networks,
and we show that with this assumption, heterogeneous degree distributions and
strong clustering in complex networks emerge naturally as simple reflections of
the negative curvature and metric property of the underlying hyperbolic
geometry. Conversely, we show that if a network has some metric structure, and
if the network degree distribution is heterogeneous, then the network has an
effective hyperbolic geometry underneath. We then establish a mapping between
our geometric framework and statistical mechanics of complex networks. This
mapping interprets edges in a network as non-interacting fermions whose
energies are hyperbolic distances between nodes, while the auxiliary fields
coupled to edges are linear functions of these energies or distances. The
geometric network ensemble subsumes the standard configuration model and
classical random graphs as two limiting cases with degenerate geometric
structures. Finally, we show that targeted transport processes without global
topology knowledge, made possible by our geometric framework, are maximally
efficient, according to all efficiency measures, in networks with strongest
heterogeneity and clustering, and that this efficiency is remarkably robust
with respect to even catastrophic disturbances and damages to the network
structure
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