5,084 research outputs found
Approximating Spectral Impact of Structural Perturbations in Large Networks
Determining the effect of structural perturbations on the eigenvalue spectra
of networks is an important problem because the spectra characterize not only
their topological structures, but also their dynamical behavior, such as
synchronization and cascading processes on networks. Here we develop a theory
for estimating the change of the largest eigenvalue of the adjacency matrix or
the extreme eigenvalues of the graph Laplacian when small but arbitrary set of
links are added or removed from the network. We demonstrate the effectiveness
of our approximation schemes using both real and artificial networks, showing
in particular that we can accurately obtain the spectral ranking of small
subgraphs. We also propose a local iterative scheme which computes the relative
ranking of a subgraph using only the connectivity information of its neighbors
within a few links. Our results may not only contribute to our theoretical
understanding of dynamical processes on networks, but also lead to practical
applications in ranking subgraphs of real complex networks.Comment: 9 pages, 3 figures, 2 table
On Large-Scale Graph Generation with Validation of Diverse Triangle Statistics at Edges and Vertices
Researchers developing implementations of distributed graph analytic
algorithms require graph generators that yield graphs sharing the challenging
characteristics of real-world graphs (small-world, scale-free, heavy-tailed
degree distribution) with efficiently calculable ground-truth solutions to the
desired output. Reproducibility for current generators used in benchmarking are
somewhat lacking in this respect due to their randomness: the output of a
desired graph analytic can only be compared to expected values and not exact
ground truth. Nonstochastic Kronecker product graphs meet these design criteria
for several graph analytics. Here we show that many flavors of triangle
participation can be cheaply calculated while generating a Kronecker product
graph. Given two medium-sized scale-free graphs with adjacency matrices and
, their Kronecker product graph has adjacency matrix . Such
graphs are highly compressible: edges are represented in memory and can be built in a distributed setting from
small data structures, making them easy to share in compressed form. Many
interesting graph calculations have worst-case complexity bounds and often these are reduced to
for Kronecker product graphs, when a Kronecker formula can be derived yielding
the sought calculation on in terms of related calculations on and .
We focus on deriving formulas for triangle participation at vertices, , a vector storing the number of triangles that every vertex is involved
in, and triangle participation at edges, , a sparse matrix storing
the number of triangles at every edge.Comment: 10 pages, 7 figures, IEEE IPDPS Graph Algorithms Building Block
Computational methods in cancer gene networking
In the past few years, many high-throughput techniques have been developed and applied to biological studies. These techniques such as “next generation” genome sequencing, chip-on-chip, microarray and so on can be used to measure gene expression and gene regulatory elements in a genome-wide scale. Moreover, as these technologies become more affordable and accessible, they have become a driving force in modern biology. As a result, huge amount biological data have been produced, with the expectation of increasing number of such datasets to be generated in the future. High-throughput data are more comprehensive and unbiased, but ‘real signals’ or biological insights, molecular mechanisms and biological principles are buried in the flood of data. In current biological studies, the bottleneck is no longer a lack of data, but the lack of ingenuity and computational means to extract biological insights and principles by integrating knowledge and high-throughput data. 

Here I am reviewing the concepts and principles of network biology and the computational methods which can be applied to cancer research. Furthermore, I am providing a practical guide for computational analysis of cancer gene networks
Information flow and cooperative control of vehicle formations
We consider the problem of cooperation among a collection of vehicles performing a shared task using intervehicle communication to coordinate their actions. Tools from algebraic graph theory prove useful in modeling the communication network and relating its topology to formation stability. We prove a Nyquist criterion that uses the eigenvalues of the graph Laplacian matrix to determine the effect of the communication topology on formation stability. We also propose a method for decentralized information exchange between vehicles. This approach realizes a dynamical system that supplies each vehicle with a common reference to be used for cooperative motion. We prove a separation principle that decomposes formation stability into two components: Stability of this is achieved information flow for the given graph and stability of an individual vehicle for the given controller. The information flow can thus be rendered highly robust to changes in the graph, enabling tight formation control despite limitations in intervehicle communication capability
COORDINATION OF LEADER-FOLLOWER MULTI-AGENT SYSTEM WITH TIME-VARYING OBJECTIVE FUNCTION
This thesis aims to introduce a new framework for the distributed control of multi-agent systems with adjustable swarm control objectives. Our goal is twofold: 1) to provide an overview to how time-varying objectives in the control of autonomous systems may be applied to the distributed control of multi-agent systems with variable autonomy level, and 2) to introduce a framework to incorporate the proposed concept to fundamental swarm behaviors such as aggregation and leader tracking. Leader-follower multi-agent systems are considered in this study, and a general form of time-dependent artificial potential function is proposed to describe the varying objectives of the system in the case of complete information exchange. Using Lyapunov methods, the stability and boundedness of the agents\u27 trajectories under single order and higher order dynamics are analyzed. Illustrative numerical simulations are presented to demonstrate the validity of our results. Then, we extend these results for multi-agent systems with limited information exchange and switching communication topology. The first steps of the realization of an experimental framework have been made with the ultimate goal of verifying the simulation results in practice
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