23,869 research outputs found
On short time existence for the planar network flow
We prove the existence of the flow by curvature of regular planar networks
starting from an initial network which is non-regular. The proof relies on a
monotonicity formula for expanding solutions and a local regularity result for
the network flow in the spirit of B. White's local regularity theorem for mean
curvature flow. We also show a pseudolocality theorem for mean curvature flow
in any codimension, assuming only that the initial submanifold can be locally
written as a graph with sufficiently small Lipschitz constant.Comment: Final version, to appear in Journal of Differential Geometry. 51
page
Anisotropic Radial Layout for Visualizing Centrality and Structure in Graphs
This paper presents a novel method for layout of undirected graphs, where
nodes (vertices) are constrained to lie on a set of nested, simple, closed
curves. Such a layout is useful to simultaneously display the structural
centrality and vertex distance information for graphs in many domains,
including social networks. Closed curves are a more general constraint than the
previously proposed circles, and afford our method more flexibility to preserve
vertex relationships compared to existing radial layout methods. The proposed
approach modifies the multidimensional scaling (MDS) stress to include the
estimation of a vertex depth or centrality field as well as a term that
penalizes discord between structural centrality of vertices and their alignment
with this carefully estimated field. We also propose a visualization strategy
for the proposed layout and demonstrate its effectiveness using three social
network datasets.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
Hierarchical characterization of complex networks
While the majority of approaches to the characterization of complex networks
has relied on measurements considering only the immediate neighborhood of each
network node, valuable information about the network topological properties can
be obtained by considering further neighborhoods. The current work discusses on
how the concepts of hierarchical node degree and hierarchical clustering
coefficient (introduced in cond-mat/0408076), complemented by new hierarchical
measurements, can be used in order to obtain a powerful set of topological
features of complex networks. The interpretation of such measurements is
discussed, including an analytical study of the hierarchical node degree for
random networks, and the potential of the suggested measurements for the
characterization of complex networks is illustrated with respect to simulations
of random, scale-free and regular network models as well as real data
(airports, proteins and word associations). The enhanced characterization of
the connectivity provided by the set of hierarchical measurements also allows
the use of agglomerative clustering methods in order to obtain taxonomies of
relationships between nodes in a network, a possibility which is also
illustrated in the current article.Comment: 19 pages, 23 figure
Multi-layer local optima networks for the analysis of advanced local search-based algorithms
A Local Optima Network (LON) is a graph model that compresses the fitness
landscape of a particular combinatorial optimization problem based on a
specific neighborhood operator and a local search algorithm. Determining which
and how landscape features affect the effectiveness of search algorithms is
relevant for both predicting their performance and improving the design
process. This paper proposes the concept of multi-layer LONs as well as a
methodology to explore these models aiming at extracting metrics for fitness
landscape analysis. Constructing such models, extracting and analyzing their
metrics are the preliminary steps into the direction of extending the study on
single neighborhood operator heuristics to more sophisticated ones that use
multiple operators. Therefore, in the present paper we investigate a twolayer
LON obtained from instances of a combinatorial problem using bitflip and swap
operators. First, we enumerate instances of NK-landscape model and use the hill
climbing heuristic to build the corresponding LONs. Then, using LON metrics, we
analyze how efficiently the search might be when combining both strategies. The
experiments show promising results and demonstrate the ability of multi-layer
LONs to provide useful information that could be used for in metaheuristics
based on multiple operators such as Variable Neighborhood Search.Comment: Accepted in GECCO202
Robustness surfaces of complex networks
Despite the robustness of complex networks has been extensively studied in
the last decade, there still lacks a unifying framework able to embrace all the
proposed metrics. In the literature there are two open issues related to this
gap: (a) how to dimension several metrics to allow their summation and (b) how
to weight each of the metrics. In this work we propose a solution for the two
aforementioned problems by defining the -value and introducing the concept
of \emph{robustness surface} (). The rationale of our proposal is to
make use of Principal Component Analysis (PCA). We firstly adjust to 1 the
initial robustness of a network. Secondly, we find the most informative
robustness metric under a specific failure scenario. Then, we repeat the
process for several percentage of failures and different realizations of the
failure process. Lastly, we join these values to form the robustness surface,
which allows the visual assessment of network robustness variability. Results
show that a network presents different robustness surfaces (i.e., dissimilar
shapes) depending on the failure scenario and the set of metrics. In addition,
the robustness surface allows the robustness of different networks to be
compared.Comment: submitted to Scientific Report
EEG sleep stages identification based on weighted undirected complex networks
Sleep scoring is important in sleep research because any errors in the scoring of the patient's sleep electroencephalography (EEG) recordings can cause serious problems such as incorrect diagnosis, medication errors, and misinterpretations of patient's EEG recordings. The aim of this research is to develop a new automatic method for EEG sleep stages classification based on a statistical model and weighted brain networks.
Methods
each EEG segment is partitioned into a number of blocks using a sliding window technique. A set of statistical features are extracted from each block. As a result, a vector of features is obtained to represent each EEG segment. Then, the vector of features is mapped into a weighted undirected network. Different structural and spectral attributes of the networks are extracted and forwarded to a least square support vector machine (LS-SVM) classifier. At the same time the network's attributes are also thoroughly investigated. It is found that the network's characteristics vary with their sleep stages. Each sleep stage is best represented using the key features of their networks.
Results
In this paper, the proposed method is evaluated using two datasets acquired from different channels of EEG (Pz-Oz and C3-A2) according to the R&K and the AASM without pre-processing the original EEG data. The obtained results by the LS-SVM are compared with those by Naïve, k-nearest and a multi-class-SVM. The proposed method is also compared with other benchmark sleep stages classification methods. The comparison results demonstrate that the proposed method has an advantage in scoring sleep stages based on single channel EEG signals.
Conclusions
An average accuracy of 96.74% is obtained with the C3-A2 channel according to the AASM standard, and 96% with the Pz-Oz channel based on the R&K standard
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