Analyzing wireless communication network vulnerability with homological invariants

This article explains how sheaves and homology theory can be applied to simplicial complex models of wireless communication networks to study their vulnerability to jamming. It develops two classes of invariants (one local and one global) for studying which nodes and links present more of a liability to the network's performance when under attack.Comment: Submitted to ICASSP 201

Information Diffusion, Facebook Clusters, and the Simplicial Model of Social Aggregation: A Computational Simulation of Simplicial Diffusers for Community Health Interventions

By integrating the simplicial model of social aggregation with existing research on opinion leadership and diffusion networks, this article introduces the constructs of simplicial diffusers (mathematically defined as nodes embedded in simplexes; a simplex is a socially bonded cluster) and simplicial diffusing sets (mathematically defined as minimal covers of a simplicial complex; a simplicial complex is a social aggregation in which socially bonded clusters are embedded) to propose a strategic approach for information diffusion of cancer screenings as a health intervention on Facebook for community cancer prevention and control. This approach is novel in its incorporation of interpersonally bonded clusters, culturally distinct subgroups, and different united social entities that co-exist within a larger community into a computational simulation to select sets of simplicial diffusers with the highest degree of information diffusion for health intervention dissemination. The unique contributions of the article also include seven propositions and five algorithmic steps for computationally modeling the simplicial model with Facebook data

Intelligent Sensor Networks

In the last decade, wireless or wired sensor networks have attracted much attention. However, most designs target general sensor network issues including protocol stack (routing, MAC, etc.) and security issues. This book focuses on the close integration of sensing, networking, and smart signal processing via machine learning. Based on their world-class research, the authors present the fundamentals of intelligent sensor networks. They cover sensing and sampling, distributed signal processing, and intelligent signal learning. In addition, they present cutting-edge research results from leading experts

Modeling and Analysis of Affiliation Networks with Subsumption

An affiliation (or two-mode) network is an abstraction commonly used for representing systems with group interactions. It consists of a set of nodes and a set of their groupings called affiliations. We introduce the notion of affiliation network with subsumption, in which no affiliation can be a subset of another. A network with this property can be modeled by an abstract simplicial complex whose facets are the affiliations of the network. We introduce a new model for generating affiliation networks with and without subsumption (represented as simplicial complexes and hypergraphs, respectively). In this model, at each iteration, a constant number of affiliations is sampled uniformly at random and then nodes are selected from these affiliations with a fixed probability. This results in an implicit preferential attachment growth and a power-law in the degree distribution (where degree is defined as the number of affiliations a node belongs to). We develop a theoretical model of this network generation procedure, prove that the degree distribution in the hypergraph case is governed by the Yule-Simon distribution, then find the exponent of its power-law tail. Similarly, we show that in the simplicial complex case, the degree distribution also has a power-law tail, and we develop a numerical technique for computing its exponent. We show that the affiliation size distributions can be concisely described via their generating functions. We develop two numerical techniques for solving the resulting functional equations, find the generating functions and compute their PMFs. Furthermore, we show that at the limit the affiliation size distribution can be approximated by a shifted Poisson or related distribution. We study the process of a giant component formation in the network, develop a theoretical estimate of the critical threshold for one of the model parameters and compare it with experiments. For a qualitative analysis of our network generation procedure, we study the average pairwise distance in the network, its assortativity, and clustering coefficient, and use Q-analysis methods to compare our networks with other synthetic networks and real-world networks

Networked Data Analytics: Network Comparison And Applied Graph Signal Processing

Networked data structures has been getting big, ubiquitous, and pervasive. As our day-to-day activities become more incorporated with and influenced by the digital world, we rely more on our intuition to provide us a high-level idea and subconscious understanding of the encountered data. This thesis aims at translating the qualitative intuitions we have about networked data into quantitative and formal tools by designing rigorous yet reasonable algorithms. In a nutshell, this thesis constructs models to compare and cluster networked data, to simplify a complicated networked structure, and to formalize the notion of smoothness and variation for domain-specific signals on a network. This thesis consists of two interrelated thrusts which explore both the scenarios where networks have intrinsic value and are themselves the object of study, and where the interest is for signals defined on top of the networks, so we leverage the information in the network to analyze the signals. Our results suggest that the intuition we have in analyzing huge data can be transformed into rigorous algorithms, and often the intuition results in superior performance, new observations, better complexity, and/or bridging two commonly implemented methods. Even though different in the principles they investigate, both thrusts are constructed on what we think as a contemporary alternation in data analytics: from building an algorithm then understanding it to having an intuition then building an algorithm around it. We show that in order to formalize the intuitive idea to measure the difference between a pair of networks of arbitrary sizes, we could design two algorithms based on the intuition to find mappings between the node sets or to map one network into the subset of another network. Such methods also lead to a clustering algorithm to categorize networked data structures. Besides, we could define the notion of frequencies of a given network by ordering features in the network according to how important they are to the overall information conveyed by the network. These proposed algorithms succeed in comparing collaboration histories of researchers, clustering research communities via their publication patterns, categorizing moving objects from uncertain measurmenets, and separating networks constructed from different processes. In the context of data analytics on top of networks, we design domain-specific tools by leveraging the recent advances in graph signal processing, which formalizes the intuitive notion of smoothness and variation of signals defined on top of networked structures, and generalizes conventional Fourier analysis to the graph domain. In specific, we show how these tools can be used to better classify the cancer subtypes by considering genetic profiles as signals on top of gene-to-gene interaction networks, to gain new insights to explain the difference between human beings in learning new tasks and switching attentions by considering brain activities as signals on top of brain connectivity networks, as well as to demonstrate how common methods in rating prediction are special graph filters and to base on this observation to design novel recommendation system algorithms

Department of Computer Science Activity 1998-2004

This report summarizes much of the research and teaching activity of the Department of Computer Science at Dartmouth College between late 1998 and late 2004. The material for this report was collected as part of the final report for NSF Institutional Infrastructure award EIA-9802068, which funded equipment and technical staff during that six-year period. This equipment and staff supported essentially all of the department\u27s research activity during that period

Measurements, Models, Systems and Design

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