Computing Scalable Multivariate Glocal Invariants of Large (Brain-) Graphs

Graphs are quickly emerging as a leading abstraction for the representation of data. One important application domain originates from an emerging discipline called "connectomics". Connectomics studies the brain as a graph; vertices correspond to neurons (or collections thereof) and edges correspond to structural or functional connections between them. To explore the variability of connectomes---to address both basic science questions regarding the structure of the brain, and medical health questions about psychiatry and neurology---one can study the topological properties of these brain-graphs. We define multivariate glocal graph invariants: these are features of the graph that capture various local and global topological properties of the graphs. We show that the collection of features can collectively be computed via a combination of daisy-chaining, sparse matrix representation and computations, and efficient approximations. Our custom open-source Python package serves as a back-end to a Web-service that we have created to enable researchers to upload graphs, and download the corresponding invariants in a number of different formats. Moreover, we built this package to support distributed processing on multicore machines. This is therefore an enabling technology for network science, lowering the barrier of entry by providing tools to biologists and analysts who otherwise lack these capabilities. As a demonstration, we run our code on 120 brain-graphs, each with approximately 16M vertices and up to 90M edges.Comment: Published as part of 2013 IEEE GlobalSIP conferenc

Multi-layer Architecture For Storing Visual Data Based on WCF and Microsoft SQL Server Database

In this paper we present a novel architecture for storing visual data. Effective storing, browsing and searching collections of images is one of the most important challenges of computer science. The design of architecture for storing such data requires a set of tools and frameworks such as SQL database management systems and service-oriented frameworks. The proposed solution is based on a multi-layer architecture, which allows to replace any component without recompilation of other components. The approach contains five components, i.e. Model, Base Engine, Concrete Engine, CBIR service and Presentation. They were based on two well-known design patterns: Dependency Injection and Inverse of Control. For experimental purposes we implemented the SURF local interest point detector as a feature extractor and $K$-means clustering as indexer. The presented architecture is intended for content-based retrieval systems simulation purposes as well as for real-world CBIR tasks.Comment: Accepted for the 14th International Conference on Artificial Intelligence and Soft Computing, ICAISC, June 14-18, 2015, Zakopane, Polan

Ergodic Control and Polyhedral approaches to PageRank Optimization

We study a general class of PageRank optimization problems which consist in finding an optimal outlink strategy for a web site subject to design constraints. We consider both a continuous problem, in which one can choose the intensity of a link, and a discrete one, in which in each page, there are obligatory links, facultative links and forbidden links. We show that the continuous problem, as well as its discrete variant when there are no constraints coupling different pages, can both be modeled by constrained Markov decision processes with ergodic reward, in which the webmaster determines the transition probabilities of websurfers. Although the number of actions turns out to be exponential, we show that an associated polytope of transition measures has a concise representation, from which we deduce that the continuous problem is solvable in polynomial time, and that the same is true for the discrete problem when there are no coupling constraints. We also provide efficient algorithms, adapted to very large networks. Then, we investigate the qualitative features of optimal outlink strategies, and identify in particular assumptions under which there exists a "master" page to which all controlled pages should point. We report numerical results on fragments of the real web graph.Comment: 39 page

A method for visualization of invariant sets of dynamical systems based on the ergodic partition

We provide an algorithm for visualization of invariant sets of dynamical systems with a smooth invariant measure. The algorithm is based on a constructive proof of the ergodic partition theorem for automorphisms of compact metric spaces. The ergodic partition of a compact metric space A, under the dynamics of a continuous automorphism T, is shown to be the product of measurable partitions of the space induced by the time averages of a set of functions on A. The numerical algorithm consists of computing the time averages of a chosen set of functions and partitioning the phase space into their level sets. The method is applied to the three-dimensional ABC map for which the dynamics was visualized by other methods in Feingold et al