Commentary on Robert Riley's article "A personal account of the discovery of hyperbolic structures on some knot complements"

We give some background and biographical commentary on the postumous article that appears in this [journal issue | ArXiv] by Robert Riley on his part of the early history of hyperbolic structures on some compact 3-manifolds. A complete list of Riley's publications appears at the end of the article.Comment: 5 page

The dynamics of quasi-isometric foliations

If the stable, center, and unstable foliations of a partially hyperbolic system are quasi-isometric, the system has Global Product Structure. This result also applies to Anosov systems and to other invariant splittings. If a partially hyperbolic system on a manifold with abelian fundamental group has quasi-isometric stable and unstable foliations, the center foliation is without holonomy. If, further, the system has Global Product Structure, then all center leaves are homeomorphic.Comment: 18 pages, 1 figur

A robust numerical method to study oscillatory instability of gap solitary waves

The spectral problem associated with the linearization about solitary waves of spinor systems or optical coupled mode equations supporting gap solitons is formulated in terms of the Evans function, a complex analytic function whose zeros correspond to eigenvalues. These problems may exhibit oscillatory instabilities where eigenvalues detach from the edges of the continuous spectrum, so called edge bifurcations. A numerical framework, based on a fast robust shooting algorithm using exterior algebra is described. The complete algorithm is robust in the sense that it does not produce spurious unstable eigenvalues. The algorithm allows to locate exactly where the unstable discrete eigenvalues detach from the continuous spectrum. Moreover, the algorithm allows for stable shooting along multi-dimensional stable and unstable manifolds. The method is illustrated by computing the stability and instability of gap solitary waves of a coupled mode model.Comment: key words: gap solitary wave, numerical Evans function, edge bifurcation, exterior algebra, oscillatory instability, massive Thirring model. accepted for publication in SIAD

The Algebra of Strand Splitting. I. A Braided Version of Thompson's Group V

We construct a braided version of Thompson's group V.Comment: 27 page

Generating Preview Tables for Entity Graphs

Users are tapping into massive, heterogeneous entity graphs for many applications. It is challenging to select entity graphs for a particular need, given abundant datasets from many sources and the oftentimes scarce information for them. We propose methods to produce preview tables for compact presentation of important entity types and relationships in entity graphs. The preview tables assist users in attaining a quick and rough preview of the data. They can be shown in a limited display space for a user to browse and explore, before she decides to spend time and resources to fetch and investigate the complete dataset. We formulate several optimization problems that look for previews with the highest scores according to intuitive goodness measures, under various constraints on preview size and distance between preview tables. The optimization problem under distance constraint is NP-hard. We design a dynamic-programming algorithm and an Apriori-style algorithm for finding optimal previews. Results from experiments, comparison with related work and user studies demonstrated the scoring measures' accuracy and the discovery algorithms' efficiency.Comment: This is the camera-ready version of a SIGMOD16 paper. There might be tiny differences in layout, spacing and linebreaking, compared with the version in the SIGMOD16 proceedings, since we must submit TeX files and use arXiv to compile the file

Towards a relation extraction framework for cyber-security concepts

In order to assist security analysts in obtaining information pertaining to their network, such as novel vulnerabilities, exploits, or patches, information retrieval methods tailored to the security domain are needed. As labeled text data is scarce and expensive, we follow developments in semi-supervised Natural Language Processing and implement a bootstrapping algorithm for extracting security entities and their relationships from text. The algorithm requires little input data, specifically, a few relations or patterns (heuristics for identifying relations), and incorporates an active learning component which queries the user on the most important decisions to prevent drifting from the desired relations. Preliminary testing on a small corpus shows promising results, obtaining precision of .82.Comment: 4 pages in Cyber & Information Security Research Conference 2015, AC

Social Ranking Techniques for the Web

The proliferation of social media has the potential for changing the structure and organization of the web. In the past, scientists have looked at the web as a large connected component to understand how the topology of hyperlinks correlates with the quality of information contained in the page and they proposed techniques to rank information contained in web pages. We argue that information from web pages and network data on social relationships can be combined to create a personalized and socially connected web. In this paper, we look at the web as a composition of two networks, one consisting of information in web pages and the other of personal data shared on social media web sites. Together, they allow us to analyze how social media tunnels the flow of information from person to person and how to use the structure of the social network to rank, deliver, and organize information specifically for each individual user. We validate our social ranking concepts through a ranking experiment conducted on web pages that users shared on Google Buzz and Twitter.Comment: 7 pages, ASONAM 201

Exposing Multi-Relational Networks to Single-Relational Network Analysis Algorithms

Many, if not most network analysis algorithms have been designed specifically for single-relational networks; that is, networks in which all edges are of the same type. For example, edges may either represent "friendship," "kinship," or "collaboration," but not all of them together. In contrast, a multi-relational network is a network with a heterogeneous set of edge labels which can represent relationships of various types in a single data structure. While multi-relational networks are more expressive in terms of the variety of relationships they can capture, there is a need for a general framework for transferring the many single-relational network analysis algorithms to the multi-relational domain. It is not sufficient to execute a single-relational network analysis algorithm on a multi-relational network by simply ignoring edge labels. This article presents an algebra for mapping multi-relational networks to single-relational networks, thereby exposing them to single-relational network analysis algorithms.Comment: ISSN:1751-157

Mindfulness and emotional regulation as sequential mediators in the relationship between attachment security and depression

Depression is a significant global health issue that has previously been associated with negative early care experiences and insecure attachment styles. This has led to much interest in identifying variables that may interrupt this relationship and prevent detrimental personal, social and economic outcomes. Recent research has indicated associations between the two seemingly distinct constructs of secure attachment and mindfulness, with similar positive outcomes. One hundred and forty eight participants completed an online survey exploring a possible sequential cognitive processing model, which predicted that higher levels of mindfulness and then emotional regulation would mediate the relationship between attachment and depression. Full mediation was found in regards to secure, preoccupied and dismissive attachment, whereas partial mediation was identified in the case of fearful attachment. The results support the possibility of an alternative cognitive processing pathway that may interrupt the association between negative early care experiences and concomitant negative mental health outcomes. Further exploration of this relationship is indicated

The Definition and Measurement of the Topological Entropy per Unit Volume in Parabolic PDE's

We define the topological entropy per unit volume in parabolic PDE's such as the complex Ginzburg-Landau equation, and show that it exists, and is bounded by the upper Hausdorff dimension times the maximal expansion rate. We then give a constructive implementation of a bound on the inertial range of such equations. Using this bound, we are able to propose a finite sampling algorithm which allows (in principle) to measure this entropy from experimental data.Comment: 26 pages, 1 small figur