40,366 research outputs found
Computation of protein geometry and its applications: Packing and function prediction
This chapter discusses geometric models of biomolecules and geometric
constructs, including the union of ball model, the weigthed Voronoi diagram,
the weighted Delaunay triangulation, and the alpha shapes. These geometric
constructs enable fast and analytical computaton of shapes of biomoleculres
(including features such as voids and pockets) and metric properties (such as
area and volume). The algorithms of Delaunay triangulation, computation of
voids and pockets, as well volume/area computation are also described. In
addition, applications in packing analysis of protein structures and protein
function prediction are also discussed.Comment: 32 pages, 9 figure
Homological Region Adjacency Tree for a 3D Binary Digital Image via HSF Model
Given a 3D binary digital image I, we define and compute
an edge-weighted tree, called Homological Region Tree (or Hom-Tree,
for short). It coincides, as unweighted graph, with the classical Region
Adjacency Tree of black 6-connected components (CCs) and white 26-
connected components of I. In addition, we define the weight of an edge
(R, S) as the number of tunnels that the CCs R and S “share”. The
Hom-Tree structure is still an isotopic invariant of I. Thus, it provides
information about how the different homology groups interact between
them, while preserving the duality of black and white CCs.
An experimentation with a set of synthetic images showing different
shapes and different complexity of connected component nesting is performed
for numerically validating the method.Ministerio de EconomĂa y Competitividad MTM2016-81030-
Characterizing the Shape of Activation Space in Deep Neural Networks
The representations learned by deep neural networks are difficult to
interpret in part due to their large parameter space and the complexities
introduced by their multi-layer structure. We introduce a method for computing
persistent homology over the graphical activation structure of neural networks,
which provides access to the task-relevant substructures activated throughout
the network for a given input. This topological perspective provides unique
insights into the distributed representations encoded by neural networks in
terms of the shape of their activation structures. We demonstrate the value of
this approach by showing an alternative explanation for the existence of
adversarial examples. By studying the topology of network activations across
multiple architectures and datasets, we find that adversarial perturbations do
not add activations that target the semantic structure of the adversarial class
as previously hypothesized. Rather, adversarial examples are explainable as
alterations to the dominant activation structures induced by the original
image, suggesting the class representations learned by deep networks are
problematically sparse on the input space
Analysing Human Mobility Patterns of Hiking Activities through Complex Network Theory
The exploitation of high volume of geolocalized data from social sport
tracking applications of outdoor activities can be useful for natural resource
planning and to understand the human mobility patterns during leisure
activities. This geolocalized data represents the selection of hike activities
according to subjective and objective factors such as personal goals, personal
abilities, trail conditions or weather conditions. In our approach, human
mobility patterns are analysed from trajectories which are generated by hikers.
We propose the generation of the trail network identifying special points in
the overlap of trajectories. Trail crossings and trailheads define our network
and shape topological features. We analyse the trail network of Balearic
Islands, as a case of study, using complex weighted network theory. The
analysis is divided into the four seasons of the year to observe the impact of
weather conditions on the network topology. The number of visited places does
not decrease despite the large difference in the number of samples of the two
seasons with larger and lower activity. It is in summer season where it is
produced the most significant variation in the frequency and localization of
activities from inland regions to coastal areas. Finally, we compare our model
with other related studies where the network possesses a different purpose. One
finding of our approach is the detection of regions with relevant importance
where landscape interventions can be applied in function of the communities.Comment: 20 pages, 9 figures, accepte
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