3,134 research outputs found
A complete classification of spatial relations using the Voronoi-based nine-intersection model
In this article we show that the Voronoi-based nine-intersection (V9I) model proposed by Chen et al. (2001, A Voronoi-based 9-intersection model for spatial relations. International Journal of Geographical Information Science, 15 (3), 201-220) is more expressive than what has been believed before. Given any two spatial entities A and B, the V9I relation between A and B is represented as a 3 × 3 Boolean matrix. For each pair of types of spatial entities that is, points, lines, and regions, we first show that most Boolean matrices do not represent a V9I relation by using topological constraints and the definition of Voronoi regions. Then, we provide illustrations for all the remaining matrices. This guarantees that our method is sound and complete. In particular, we show that there are 18 V9I relations between two areas with connected interior, while there are only nine four-intersection relations. Our investigations also show that, unlike many other spatial relation models, V9I relations are context or shape sensitive. That is, the existence of other entities or the shape of the entities may affect the validity of certain relations. © 2013 Taylor & Francis
The Spine of the Cosmic Web
We present the SpineWeb framework for the topological analysis of the Cosmic
Web and the identification of its walls, filaments and cluster nodes. Based on
the watershed segmentation of the cosmic density field, the SpineWeb method
invokes the local adjacency properties of the boundaries between the watershed
basins to trace the critical points in the density field and the separatrices
defined by them. The separatrices are classified into walls and the spine, the
network of filaments and nodes in the matter distribution. Testing the method
with a heuristic Voronoi model yields outstanding results. Following the
discussion of the test results, we apply the SpineWeb method to a set of
cosmological N-body simulations. The latter illustrates the potential for
studying the structure and dynamics of the Cosmic Web.Comment: Accepted for publication HIGH-RES version:
http://skysrv.pha.jhu.edu/~miguel/SpineWeb
Uncovering the spatial structure of mobility networks
The extraction of a clear and simple footprint of the structure of large,
weighted and directed networks is a general problem that has many applications.
An important example is given by origin-destination matrices which contain the
complete information on commuting flows, but are difficult to analyze and
compare. We propose here a versatile method which extracts a coarse-grained
signature of mobility networks, under the form of a matrix that
separates the flows into four categories. We apply this method to
origin-destination matrices extracted from mobile phone data recorded in
thirty-one Spanish cities. We show that these cities essentially differ by
their proportion of two types of flows: integrated (between residential and
employment hotspots) and random flows, whose importance increases with city
size. Finally the method allows to determine categories of networks, and in the
mobility case to classify cities according to their commuting structure.Comment: 10 pages, 5 figures +Supplementary informatio
Mobile Communication Signatures of Unemployment
The mapping of populations socio-economic well-being is highly constrained by
the logistics of censuses and surveys. Consequently, spatially detailed changes
across scales of days, weeks, or months, or even year to year, are difficult to
assess; thus the speed of which policies can be designed and evaluated is
limited. However, recent studies have shown the value of mobile phone data as
an enabling methodology for demographic modeling and measurement. In this work,
we investigate whether indicators extracted from mobile phone usage can reveal
information about the socio-economical status of microregions such as districts
(i.e., average spatial resolution < 2.7km). For this we examine anonymized
mobile phone metadata combined with beneficiaries records from unemployment
benefit program. We find that aggregated activity, social, and mobility
patterns strongly correlate with unemployment. Furthermore, we construct a
simple model to produce accurate reconstruction of district level unemployment
from their mobile communication patterns alone. Our results suggest that
reliable and cost-effective economical indicators could be built based on
passively collected and anonymized mobile phone data. With similar data being
collected every day by telecommunication services across the world,
survey-based methods of measuring community socioeconomic status could
potentially be augmented or replaced by such passive sensing methods in the
future
On Random Bubble Lattices
We study random bubble lattices which can be produced by processes such as
first order phase transitions, and derive characteristics that are important
for understanding the percolation of distinct varieties of bubbles. The results
are relevant to the formation of topological defects as they show that infinite
domain walls and strings will be produced during appropriate first order
transitions, and that the most suitable regular lattice to study defect
formation in three dimensions is a face centered cubic lattice. Another
application of our work is to the distribution of voids in the large-scale
structure of the universe. We argue that the present universe is more akin to a
system undergoing a first-order phase transition than to one that is
crystallizing, as is implicit in the Voronoi foam description. Based on the
picture of a bubbly universe, we predict a mean coordination number for the
voids of 13.4. The mean coordination number may also be used as a tool to
distinguish between different scenarios for structure formation.Comment: several modifications including new abstract, comparison with froth
models, asymptotics of coordination number distribution, further discussion
of biased defects, and relevance to large-scale structur
Central limit theorems for Poisson hyperplane tessellations
We derive a central limit theorem for the number of vertices of convex
polytopes induced by stationary Poisson hyperplane processes in .
This result generalizes an earlier one proved by Paroux [Adv. in Appl. Probab.
30 (1998) 640--656] for intersection points of motion-invariant Poisson line
processes in . Our proof is based on Hoeffding's decomposition of
-statistics which seems to be more efficient and adequate to tackle the
higher-dimensional case than the ``method of moments'' used in [Adv. in Appl.
Probab. 30 (1998) 640--656] to treat the case . Moreover, we extend our
central limit theorem in several directions. First we consider -flat
processes induced by Poisson hyperplane processes in for . Second we derive (asymptotic) confidence intervals for the
intensities of these -flat processes and, third, we prove multivariate
central limit theorems for the -dimensional joint vectors of numbers of
-flats and their -volumes, respectively, in an increasing spherical
region.Comment: Published at http://dx.doi.org/10.1214/105051606000000033 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Deep Interactive Region Segmentation and Captioning
With recent innovations in dense image captioning, it is now possible to
describe every object of the scene with a caption while objects are determined
by bounding boxes. However, interpretation of such an output is not trivial due
to the existence of many overlapping bounding boxes. Furthermore, in current
captioning frameworks, the user is not able to involve personal preferences to
exclude out of interest areas. In this paper, we propose a novel hybrid deep
learning architecture for interactive region segmentation and captioning where
the user is able to specify an arbitrary region of the image that should be
processed. To this end, a dedicated Fully Convolutional Network (FCN) named
Lyncean FCN (LFCN) is trained using our special training data to isolate the
User Intention Region (UIR) as the output of an efficient segmentation. In
parallel, a dense image captioning model is utilized to provide a wide variety
of captions for that region. Then, the UIR will be explained with the caption
of the best match bounding box. To the best of our knowledge, this is the first
work that provides such a comprehensive output. Our experiments show the
superiority of the proposed approach over state-of-the-art interactive
segmentation methods on several well-known datasets. In addition, replacement
of the bounding boxes with the result of the interactive segmentation leads to
a better understanding of the dense image captioning output as well as accuracy
enhancement for the object detection in terms of Intersection over Union (IoU).Comment: 17, pages, 9 figure
Limit theorems for functionals on the facets of stationary random tessellations
We observe stationary random tessellations in
through a convex sampling window that expands unboundedly
and we determine the total -volume of those -dimensional manifold
processes which are induced on the -facets of () by their
intersections with the -facets of independent and identically
distributed motion-invariant tessellations generated within each cell
of . The cases of being either a Poisson hyperplane tessellation
or a random tessellation with weak dependences are treated separately. In both
cases, however, we obtain that all of the total volumes measured in are
approximately normally distributed when is sufficiently large. Structural
formulae for mean values and asymptotic variances are derived and explicit
numerical values are given for planar Poisson--Voronoi tessellations (PVTs) and
Poisson line tessellations (PLTs).Comment: Published at http://dx.doi.org/10.3150/07-BEJ6131 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Foundations of Dissipative Particle Dynamics
We derive a mesoscopic modeling and simulation technique that is very close
to the technique known as dissipative particle dynamics. The model is derived
from molecular dynamics by means of a systematic coarse-graining procedure.
Thus the rules governing our new form of dissipative particle dynamics reflect
the underlying molecular dynamics; in particular all the underlying
conservation laws carry over from the microscopic to the mesoscopic
descriptions. Whereas previously the dissipative particles were spheres of
fixed size and mass, now they are defined as cells on a Voronoi lattice with
variable masses and sizes. This Voronoi lattice arises naturally from the
coarse-graining procedure which may be applied iteratively and thus represents
a form of renormalisation-group mapping. It enables us to select any desired
local scale for the mesoscopic description of a given problem. Indeed, the
method may be used to deal with situations in which several different length
scales are simultaneously present. Simulations carried out with the present
scheme show good agreement with theoretical predictions for the equilibrium
behavior.Comment: 18 pages, 7 figure
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