The pathogenic role of the inflammasome in neurodegenerative diseases

The inflammasome is a large macromolecular complex that contains multiple copies of a receptor or sensor of pathogen-derived or damage-derived molecular patterns, pro-caspase-1, and an adaptor called ASC (apoptotic speck containing protein with a CARD), which results in caspase-1 maturation. Caspase-1 then mediates the release of pro-inflammatory cytokines such as IL-1β and IL-18. These cytokines play critical roles in mediating immune responses during inflammation and innate immunity. Broader studies of the inflammasome over the years have implicated their roles in the pathogenesis of a variety of inflammatory diseases. Recently, studies have shown that the inflammasome modulates neuroinflammatory cells and the initial stages of neuroinflammation. A secondary cascade of events associated with neuroinflammation (such as oxidative stress) has been shown to activate the inflammasome, making the inflammasome a promising therapeutic target in the modulation of neurodegenerative diseases. This review will focus on the pathogenic role that inflammasomes play in neurologic diseases such as Alzheimer's disease, traumatic brain injury, and multiple sclerosis

The Irreducible Spine(s) of Undirected Networks

Using closure concepts, we show that within every undirected network, or graph, there is a unique irreducible subgraph which we call its "spine". The chordless cycles which comprise this irreducible core effectively characterize the connectivity structure of the network as a whole. In particular, it is shown that the center of the network, whether defined by distance or betweenness centrality, is effectively contained in this spine. By counting the number of cycles of length 3 <= k <= max_length, we can also create a kind of signature that can be used to identify the network. Performance is analyzed, and the concepts we develop are illurstrated by means of a relatively small running sample network of about 400 nodes.Comment: Submitted to WISE 201

Topology of Cell-Aggregated Planar Graphs

We present new algorithm for growth of non-clustered planar graphs by aggregation of cells with given distribution of size and constraint of connectivity k=3 per node. The emergent graph structures are controlled by two parameters--chemical potential of the cell aggregation and the width of the cell size distribution. We compute several statistical properties of these graphs--fractal dimension of the perimeter, distribution of shortest paths between pairs of nodes and topological betweenness of nodes and links. We show how these topological properties depend on the control parameters of the aggregation process and discuss their relevance for the conduction of current in self-assembled nanopatterns.Comment: 8 pages, 5 figure

Distance, dissimilarity index, and network community structure

We address the question of finding the community structure of a complex network. In an earlier effort [H. Zhou, {\em Phys. Rev. E} (2003)], the concept of network random walking is introduced and a distance measure defined. Here we calculate, based on this distance measure, the dissimilarity index between nearest-neighboring vertices of a network and design an algorithm to partition these vertices into communities that are hierarchically organized. Each community is characterized by an upper and a lower dissimilarity threshold. The algorithm is applied to several artificial and real-world networks, and excellent results are obtained. In the case of artificially generated random modular networks, this method outperforms the algorithm based on the concept of edge betweenness centrality. For yeast's protein-protein interaction network, we are able to identify many clusters that have well defined biological functions.Comment: 10 pages, 7 figures, REVTeX4 forma

Resistance distance, information centrality, node vulnerability and vibrations in complex networks

We discuss three seemingly unrelated quantities that have been introduced in different fields of science for complex networks. The three quantities are the resistance distance, the information centrality and the node displacement. We first prove various relations among them. Then we focus on the node displacement, showing its usefulness as an index of node vulnerability.We argue that the node displacement has a better resolution as a measure of node vulnerability than the degree and the information centrality

Boxicity of graphs on surfaces

The boxicity of a graph $G=(V,E)$ is the least integer $k$ for which there exist $k$ interval graphs $G_i=(V,E_i)$, $1 \le i \le k$, such that $E=E_1 \cap ... \cap E_k$. Scheinerman proved in 1984 that outerplanar graphs have boxicity at most two and Thomassen proved in 1986 that planar graphs have boxicity at most three. In this note we prove that the boxicity of toroidal graphs is at most 7, and that the boxicity of graphs embeddable in a surface $\Sigma$ of genus $g$ is at most $5g+3$. This result yields improved bounds on the dimension of the adjacency poset of graphs on surfaces.Comment: 9 pages, 2 figure

Network Landscape from a Brownian Particle's Perspective

Given a complex biological or social network, how many clusters should it be decomposed into? We define the distance $d_{i,j}$ from node $i$ to node $j$ as the average number of steps a Brownian particle takes to reach $j$ from $i$. Node $j$ is a global attractor of $i$ if $d_{i,j}\leq d_{i,k}$ for any $k$ of the graph; it is a local attractor of $i$, if $j\in E_i$ (the set of nearest-neighbors of $i$) and $d_{i,j}\leq d_{i,l}$ for any $l\in E_i$. Based on the intuition that each node should have a high probability to be in the same community as its global (local) attractor on the global (local) scale, we present a simple method to uncover a network's community structure. This method is applied to several real networks and some discussion on its possible extensions is made.Comment: 5 pages, 4 color-figures. REVTeX 4 format. To appear in PR

Edge overload breakdown in evolving networks

We investigate growing networks based on Barabasi and Albert's algorithm for generating scale-free networks, but with edges sensitive to overload breakdown. the load is defined through edge betweenness centrality. We focus on the situation where the average number of connections per vertex is, as the number of vertices, linearly increasing in time. After an initial stage of growth, the network undergoes avalanching breakdowns to a fragmented state from which it never recovers. This breakdown is much less violent if the growth is by random rather than preferential attachment (as defines the Barabasi and Albert model). We briefly discuss the case where the average number of connections per vertex is constant. In this case no breakdown avalanches occur. Implications to the growth of real-world communication networks are discussed.Comment: To appear in Phys. Rev.