1,429 research outputs found
Multifractal Properties of the Random Resistor Network
We study the multifractal spectrum of the current in the two-dimensional
random resistor network at the percolation threshold. We consider two ways of
applying the voltage difference: (i) two parallel bars, and (ii) two points.
Our numerical results suggest that in the infinite system limit, the
probability distribution behaves for small current i as P(i) ~ 1/i. As a
consequence, the moments of i of order q less than q_c=0 do not exist and all
current of value below the most probable one have the fractal dimension of the
backbone. The backbone can thus be described in terms of only (i) blobs of
fractal dimension d_B and (ii) high current carrying bonds of fractal dimension
going from to d_B.Comment: 4 pages, 6 figures; 1 reference added; to appear in Phys. Rev. E
(Rapid Comm
Fractal dimension and size scaling of domains in thin films of multiferroic BiFeO3
We have analyzed the morphology of ferroelectric domains in very thin films
of multiferroic BiFeO3. Unlike the more common stripe domains observed in
thicker films BiFeO3 or in other ferroics, the domains tend not to be straight,
but irregular in shape, with significant domain wall roughening leading to a
fractal dimensionality. Also contrary to what is usually observed in other
ferroics, the domain size appears not to scale as the square root of the film
thickness. A model is proposed in which the observed domain size as a function
of film thickness can be directly linked to the fractal dimension of the
domains.Comment: 4 pages, 3 figure
Exact results and scaling properties of small-world networks
We study the distribution function for minimal paths in small-world networks.
Using properties of this distribution function, we derive analytic results
which greatly simplify the numerical calculation of the average minimal
distance, , and its variance, . We also discuss the
scaling properties of the distribution function. Finally, we study the limit of
large system sizes and obtain some analytic results.Comment: RevTeX, 4 pages, 5 figures included. Minor corrections and addition
Resolution limit in community detection
Detecting community structure is fundamental to clarify the link between
structure and function in complex networks and is used for practical
applications in many disciplines. A successful method relies on the
optimization of a quantity called modularity [Newman and Girvan, Phys. Rev. E
69, 026113 (2004)], which is a quality index of a partition of a network into
communities. We find that modularity optimization may fail to identify modules
smaller than a scale which depends on the total number L of links of the
network and on the degree of interconnectedness of the modules, even in cases
where modules are unambiguously defined. The probability that a module conceals
well-defined substructures is the highest if the number of links internal to
the module is of the order of \sqrt{2L} or smaller. We discuss the practical
consequences of this result by analyzing partitions obtained through modularity
optimization in artificial and real networks.Comment: 8 pages, 3 figures. Clarification of definition of community in
Section II + minor revision
Elementary processes governing the evolution of road networks
Urbanisation is a fundamental phenomenon whose quantitative characterisation
is still inadequate. We report here the empirical analysis of a unique data set
regarding almost 200 years of evolution of the road network in a large area
located north of Milan (Italy). We find that urbanisation is characterised by
the homogenisation of cell shapes, and by the stability throughout time of
high-centrality roads which constitute the backbone of the urban structure,
confirming the importance of historical paths. We show quantitatively that the
growth of the network is governed by two elementary processes: (i)
`densification', corresponding to an increase in the local density of roads
around existing urban centres and (ii) `exploration', whereby new roads trigger
the spatial evolution of the urbanisation front. The empirical identification
of such simple elementary mechanisms suggests the existence of general, simple
properties of urbanisation and opens new directions for its modelling and
quantitative description.Comment: 10 pages, 6 figure
Higher gait variability is associated with decreased parietal gray matter volume among healthy older adults
The objectives of this study were to examine the association of stride time variability (STV) with gray and white matter volumes in healthy older adults, and to determine the specific location of any parenchymal loss associated with higher STV. A total of 71 participants (mean age 69.0 +/- 0.8 years; 59.7 % female) were included in this study. All participants had a 1.0 Tesla 3D T1-weighted MRI of the brain to measure gray and white matter volumes. STV was measured at steady-state self-selected walking speed using an electronic footswitch system. We found an association between higher STV and lower gray matter volume in the right parietal lobe (e.g., angular gyrus, Brodmann area 39, cluster corrected pFWE = 0.035). There were no significant associations between STV and higher gray matter volume or change in white matter volume. To the best of our knowledge this study is the first to identify a significant association of higher STV with lower right parietal gray matter volume in healthy older adults
Spatial correlations in attribute communities
Community detection is an important tool for exploring and classifying the
properties of large complex networks and should be of great help for spatial
networks. Indeed, in addition to their location, nodes in spatial networks can
have attributes such as the language for individuals, or any other
socio-economical feature that we would like to identify in communities. We
discuss in this paper a crucial aspect which was not considered in previous
studies which is the possible existence of correlations between space and
attributes. Introducing a simple toy model in which both space and node
attributes are considered, we discuss the effect of space-attribute
correlations on the results of various community detection methods proposed for
spatial networks in this paper and in previous studies. When space is
irrelevant, our model is equivalent to the stochastic block model which has
been shown to display a detectability-non detectability transition. In the
regime where space dominates the link formation process, most methods can fail
to recover the communities, an effect which is particularly marked when
space-attributes correlations are strong. In this latter case, community
detection methods which remove the spatial component of the network can miss a
large part of the community structure and can lead to incorrect results.Comment: 10 pages and 7 figure
- …