Network Community Detection on Metric Space

Community detection in a complex network is an important problem of much interest in recent years. In general, a community detection algorithm chooses an objective function and captures the communities of the network by optimizing the objective function, and then, one uses various heuristics to solve the optimization problem to extract the interesting communities for the user. In this article, we demonstrate the procedure to transform a graph into points of a metric space and develop the methods of community detection with the help of a metric defined for a pair of points. We have also studied and analyzed the community structure of the network therein. The results obtained with our approach are very competitive with most of the well-known algorithms in the literature, and this is justified over the large collection of datasets. On the other hand, it can be observed that time taken by our algorithm is quite less compared to other methods and justifies the theoretical findings

Predicting protein functions with message passing algorithms

Motivation: In the last few years a growing interest in biology has been shifting towards the problem of optimal information extraction from the huge amount of data generated via large scale and high-throughput techniques. One of the most relevant issues has recently become that of correctly and reliably predicting the functions of observed but still functionally undetermined proteins starting from information coming from the network of co-observed proteins of known functions. Method: The method proposed in this article is based on a message passing algorithm known as Belief Propagation, which takes as input the network of proteins physical interactions and a catalog of known proteins functions, and returns the probabilities for each unclassified protein of having one chosen function. The implementation of the algorithm allows for fast on-line analysis, and can be easily generalized to more complex graph topologies taking into account hyper-graphs, {\em i.e.} complexes of more than two interacting proteins.Comment: 12 pages, 9 eps figures, 1 additional html tabl

Joint Centrality Distinguishes Optimal Leaders in Noisy Networks

We study the performance of a network of agents tasked with tracking an external unknown signal in the presence of stochastic disturbances and under the condition that only a limited subset of agents, known as leaders, can measure the signal directly. We investigate the optimal leader selection problem for a prescribed maximum number of leaders, where the optimal leader set minimizes total system error defined as steady-state variance about the external signal. In contrast to previously established greedy algorithms for optimal leader selection, our results rely on an expression of total system error in terms of properties of the underlying network graph. We demonstrate that the performance of any given set of leaders depends on their influence as determined by a new graph measure of centrality of a set. We define the $joint \; centrality$ of a set of nodes in a network graph such that a leader set with maximal joint centrality is an optimal leader set. In the case of a single leader, we prove that the optimal leader is the node with maximal information centrality. In the case of multiple leaders, we show that the nodes in the optimal leader set balance high information centrality with a coverage of the graph. For special cases of graphs, we solve explicitly for optimal leader sets. We illustrate with examples.Comment: Conditionally accepted to IEEE TCN

Model Predictive Control Based Trajectory Generation for Autonomous Vehicles - An Architectural Approach

Research in the field of automated driving has created promising results in the last years. Some research groups have shown perception systems which are able to capture even complicated urban scenarios in great detail. Yet, what is often missing are general-purpose path- or trajectory planners which are not designed for a specific purpose. In this paper we look at path- and trajectory planning from an architectural point of view and show how model predictive frameworks can contribute to generalized path- and trajectory generation approaches for generating safe trajectories even in cases of system failures.Comment: Presented at IEEE Intelligent Vehicles Symposium 2017, Los Angeles, CA, US