3,871 research outputs found
The diplomat's dilemma: Maximal power for minimal effort in social networks
Closeness is a global measure of centrality in networks, and a proxy for how
influential actors are in social networks. In most network models, and many
empirical networks, closeness is strongly correlated with degree. However, in
social networks there is a cost of maintaining social ties. This leads to a
situation (that can occur in the professional social networks of executives,
lobbyists, diplomats and so on) where agents have the conflicting objectives of
aiming for centrality while simultaneously keeping the degree low. We
investigate this situation in an adaptive network-evolution model where agents
optimize their positions in the network following individual strategies, and
using only local information. The strategies are also optimized, based on the
success of the agent and its neighbors. We measure and describe the time
evolution of the network and the agents' strategies.Comment: Submitted to Adaptive Networks: Theory, Models and Applications, to
be published from Springe
Towards a genome-wide transcriptogram: the Saccharomyces cerevisiae case
A genome modular classification that associates cellular processes to modules could lead to a method to quantify the differences in gene expression levels in different cellular stages or conditions: the transcriptogram, a powerful tool for assessing cell performance, would be at hand. Here we present a computational method to order genes on a line that clusters strongly interacting genes, defining functional modules associated with gene ontology terms. The starting point is a list of genes and a matrix specifying their interactions, available at large gene interaction databases. Considering the Saccharomyces cerevisiae genome we produced a succession of plots of gene transcription levels for a fermentation process. These plots discriminate the fermentation stage the cell is going through and may be regarded as the first versions of a transcriptogram. This method is useful for extracting information from cell stimuli/responses experiments, and may be applied with diagnostic purposes to different organisms
Hamiltonian System Approach to Distributed Spectral Decomposition in Networks
Because of the significant increase in size and complexity of the networks,
the distributed computation of eigenvalues and eigenvectors of graph matrices
has become very challenging and yet it remains as important as before. In this
paper we develop efficient distributed algorithms to detect, with higher
resolution, closely situated eigenvalues and corresponding eigenvectors of
symmetric graph matrices. We model the system of graph spectral computation as
physical systems with Lagrangian and Hamiltonian dynamics. The spectrum of
Laplacian matrix, in particular, is framed as a classical spring-mass system
with Lagrangian dynamics. The spectrum of any general symmetric graph matrix
turns out to have a simple connection with quantum systems and it can be thus
formulated as a solution to a Schr\"odinger-type differential equation. Taking
into account the higher resolution requirement in the spectrum computation and
the related stability issues in the numerical solution of the underlying
differential equation, we propose the application of symplectic integrators to
the calculation of eigenspectrum. The effectiveness of the proposed techniques
is demonstrated with numerical simulations on real-world networks of different
sizes and complexities
Eigenvector Synchronization, Graph Rigidity and the Molecule Problem
The graph realization problem has received a great deal of attention in
recent years, due to its importance in applications such as wireless sensor
networks and structural biology. In this paper, we extend on previous work and
propose the 3D-ASAP algorithm, for the graph realization problem in
, given a sparse and noisy set of distance measurements. 3D-ASAP
is a divide and conquer, non-incremental and non-iterative algorithm, which
integrates local distance information into a global structure determination.
Our approach starts with identifying, for every node, a subgraph of its 1-hop
neighborhood graph, which can be accurately embedded in its own coordinate
system. In the noise-free case, the computed coordinates of the sensors in each
patch must agree with their global positioning up to some unknown rigid motion,
that is, up to translation, rotation and possibly reflection. In other words,
to every patch there corresponds an element of the Euclidean group Euc(3) of
rigid transformations in , and the goal is to estimate the group
elements that will properly align all the patches in a globally consistent way.
Furthermore, 3D-ASAP successfully incorporates information specific to the
molecule problem in structural biology, in particular information on known
substructures and their orientation. In addition, we also propose 3D-SP-ASAP, a
faster version of 3D-ASAP, which uses a spectral partitioning algorithm as a
preprocessing step for dividing the initial graph into smaller subgraphs. Our
extensive numerical simulations show that 3D-ASAP and 3D-SP-ASAP are very
robust to high levels of noise in the measured distances and to sparse
connectivity in the measurement graph, and compare favorably to similar
state-of-the art localization algorithms.Comment: 49 pages, 8 figure
A Graph-Based Semi-Supervised k Nearest-Neighbor Method for Nonlinear Manifold Distributed Data Classification
Nearest Neighbors (NN) is one of the most widely used supervised
learning algorithms to classify Gaussian distributed data, but it does not
achieve good results when it is applied to nonlinear manifold distributed data,
especially when a very limited amount of labeled samples are available. In this
paper, we propose a new graph-based NN algorithm which can effectively
handle both Gaussian distributed data and nonlinear manifold distributed data.
To achieve this goal, we first propose a constrained Tired Random Walk (TRW) by
constructing an -level nearest-neighbor strengthened tree over the graph,
and then compute a TRW matrix for similarity measurement purposes. After this,
the nearest neighbors are identified according to the TRW matrix and the class
label of a query point is determined by the sum of all the TRW weights of its
nearest neighbors. To deal with online situations, we also propose a new
algorithm to handle sequential samples based a local neighborhood
reconstruction. Comparison experiments are conducted on both synthetic data
sets and real-world data sets to demonstrate the validity of the proposed new
NN algorithm and its improvements to other version of NN algorithms.
Given the widespread appearance of manifold structures in real-world problems
and the popularity of the traditional NN algorithm, the proposed manifold
version NN shows promising potential for classifying manifold-distributed
data.Comment: 32 pages, 12 figures, 7 table
Robust Temporally Coherent Laplacian Protrusion Segmentation of 3D Articulated Bodies
In motion analysis and understanding it is important to be able to fit a
suitable model or structure to the temporal series of observed data, in order
to describe motion patterns in a compact way, and to discriminate between them.
In an unsupervised context, i.e., no prior model of the moving object(s) is
available, such a structure has to be learned from the data in a bottom-up
fashion. In recent times, volumetric approaches in which the motion is captured
from a number of cameras and a voxel-set representation of the body is built
from the camera views, have gained ground due to attractive features such as
inherent view-invariance and robustness to occlusions. Automatic, unsupervised
segmentation of moving bodies along entire sequences, in a temporally-coherent
and robust way, has the potential to provide a means of constructing a
bottom-up model of the moving body, and track motion cues that may be later
exploited for motion classification. Spectral methods such as locally linear
embedding (LLE) can be useful in this context, as they preserve "protrusions",
i.e., high-curvature regions of the 3D volume, of articulated shapes, while
improving their separation in a lower dimensional space, making them in this
way easier to cluster. In this paper we therefore propose a spectral approach
to unsupervised and temporally-coherent body-protrusion segmentation along time
sequences. Volumetric shapes are clustered in an embedding space, clusters are
propagated in time to ensure coherence, and merged or split to accommodate
changes in the body's topology. Experiments on both synthetic and real
sequences of dense voxel-set data are shown. This supports the ability of the
proposed method to cluster body-parts consistently over time in a totally
unsupervised fashion, its robustness to sampling density and shape quality, and
its potential for bottom-up model constructionComment: 31 pages, 26 figure
Revisiting the Edge of Chaos: Evolving Cellular Automata to Perform Computations
We present results from an experiment similar to one performed by Packard
(1988), in which a genetic algorithm is used to evolve cellular automata (CA)
to perform a particular computational task. Packard examined the frequency of
evolved CA rules as a function of Langton's lambda parameter (Langton, 1990),
and interpreted the results of his experiment as giving evidence for the
following two hypotheses: (1) CA rules able to perform complex computations are
most likely to be found near ``critical'' lambda values, which have been
claimed to correlate with a phase transition between ordered and chaotic
behavioral regimes for CA; (2) When CA rules are evolved to perform a complex
computation, evolution will tend to select rules with lambda values close to
the critical values. Our experiment produced very different results, and we
suggest that the interpretation of the original results is not correct. We also
review and discuss issues related to lambda, dynamical-behavior classes, and
computation in CA. The main constructive results of our study are identifying
the emergence and competition of computational strategies and analyzing the
central role of symmetries in an evolutionary system. In particular, we
demonstrate how symmetry breaking can impede the evolution toward higher
computational capability.Comment: 38 pages, compressed .ps files (780Kb) available ONLY thru anonymous
ftp. (Instructions available via `get 9303003' .
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