A New Framework for Network Disruption

Traditional network disruption approaches focus on disconnecting or lengthening paths in the network. We present a new framework for network disruption that attempts to reroute flow through critical vertices via vertex deletion, under the assumption that this will render those vertices vulnerable to future attacks. We define the load on a critical vertex to be the number of paths in the network that must flow through the vertex. We present graph-theoretic and computational techniques to maximize this load, firstly by removing either a single vertex from the network, secondly by removing a subset of vertices.Comment: Submitted for peer review on September 13, 201

GUBS: Graph-Based Unsupervised Brain Segmentation in MRI Images

Brain segmentation in magnetic resonance imaging (MRI) images is the process of isolating the brain from non-brain tissues to simplify the further analysis, such as detecting pathology or calculating volumes. This paper proposes a Graph-based Unsupervised Brain Segmentation (GUBS) that processes 3D MRI images and segments them into brain, non-brain tissues, and backgrounds. GUBS first constructs an adjacency graph from a preprocessed MRI image, weights it by the difference between voxel intensities, and computes its minimum spanning tree (MST). It then uses domain knowledge about the different regions of MRIs to sample representative points from the brain, non-brain, and background regions of the MRI image. The adjacency graph nodes corresponding to sampled points in each region are identified and used as the terminal nodes for paths connecting the regions in the MST. GUBS then computes a subgraph of the MST by first removing the longest edge of the path connecting the terminal nodes in the brain and other regions, followed by removing the longest edge of the path connecting non-brain and background regions. This process results in three labeled, connected components, whose labels are used to segment the brain, non-brain tissues, and the background. GUBS was tested by segmenting 3D T1 weighted MRI images from three publicly available data sets. GUBS shows comparable results to the state-of-the-art methods in terms of performance. However, many competing methods rely on having labeled data available for training. Labeling is a time-intensive and costly process, and a big advantage of GUBS is that it does not require labels.publishedVersio

Graph Grammars, Insertion Lie Algebras, and Quantum Field Theory

Graph grammars extend the theory of formal languages in order to model distributed parallelism in theoretical computer science. We show here that to certain classes of context-free and context-sensitive graph grammars one can associate a Lie algebra, whose structure is reminiscent of the insertion Lie algebras of quantum field theory. We also show that the Feynman graphs of quantum field theories are graph languages generated by a theory dependent graph grammar.Comment: 19 pages, LaTeX, 3 jpeg figure

Paradigm and paradox in power networks

Well known in the theory of network flows, Braess paradox states that adding path(s) to a congested road network may increase overall journey time. In transportation networks, the phenomenon results from selfish routing. In power systems, an analogous increase in congestion can arise as a consequence of Kirchhoff's laws, suggesting opportunities to optimize grid topology. The thesis starts with the discussion of Braess-like congestion phenomena in linear circuits. We prove that adding electrical path(s) always increases congestion in networks powered by voltage sources, while the opposite in networks driven by current sources. Although such predictability is not present in networks controlled by a mixture of voltage and current sources, our results offer a clean decomposition that completely separates the effect of current sources and voltage sources on total loss. The culmination of this research is a set of four equivalent methods of computing I^2R loss in mixed-source networks. We go on to explore network decomposition in combination with greedy sequential line switching heuristics to address the NP-hardness of power grid topology control. By means of some low order examples, it is shown that within a reasonably large class of greedy heuristics, none can be found that perform better than the others across all grid topologies. Despite this cautionary tale, statistical evidence indicates that, among three most representative heuristics, the global greedy heuristic is most computationally intensive but has the best chance of reducing generation cost while enforcing connectivity. The final part of the thesis presents a new approach to grid decomposition using vertex cut sets. We show that each vertex cut set and corresponding grid decomposition establishes a natural upper bound on the interactions between subgrids as nodal injections are regulated within each. Using such decomposition, it becomes possible to isolate congestion effects to a relatively small subgrid. A fast grid decomposition heuristic based on vertex cut sets and locational marginal prices is then proposed and studied through simulations on IEEE 118-bus system. On average, the computational cost is significantly reduced and the generation cost saving is similar to what is obtained with a global greedy algorithm