Mixing patterns and community structure in networks

Common experience suggests that many networks might possess community structure - division of vertices into groups, with a higher density of edges within groups than between them. Here we describe a new computer algorithm that detects structure of this kind. We apply the algorithm to a number of real-world networks and show that they do indeed possess non-trivial community structure. We suggest a possible explanation for this structure in the mechanism of assortative mixing, which is the preferential association of network vertices with others that are like them in some way. We show by simulation that this mechanism can indeed account for community structure. We also look in detail at one particular example of assortative mixing, namely mixing by vertex degree, in which vertices with similar degree prefer to be connected to one another. We propose a measure for mixing of this type which we apply to a variety of networks, and also discuss the implications for network structure and the formation of a giant component in assortatively mixed networks.Comment: 21 pages, 9 postscript figures, 2 table

Brane Tilings and Exceptional Collections

Both brane tilings and exceptional collections are useful tools for describing the low energy gauge theory on a stack of D3-branes probing a Calabi-Yau singularity. We provide a dictionary that translates between these two heretofore unconnected languages. Given a brane tiling, we compute an exceptional collection of line bundles associated to the base of the non-compact Calabi-Yau threefold. Given an exceptional collection, we derive the periodic quiver of the gauge theory which is the graph theoretic dual of the brane tiling. Our results give new insight to the construction of quiver theories and their relation to geometry.Comment: 46 pages, 37 figures, JHEP3; v2: reference added, figure 13 correcte

Cutwidth: obstructions and algorithmic aspects

Cutwidth is one of the classic layout parameters for graphs. It measures how well one can order the vertices of a graph in a linear manner, so that the maximum number of edges between any prefix and its complement suffix is minimized. As graphs of cutwidth at most $k$ are closed under taking immersions, the results of Robertson and Seymour imply that there is a finite list of minimal immersion obstructions for admitting a cut layout of width at most $k$. We prove that every minimal immersion obstruction for cutwidth at most $k$ has size at most $2^{O(k^3\log k)}$. As an interesting algorithmic byproduct, we design a new fixed-parameter algorithm for computing the cutwidth of a graph that runs in time $2^{O(k^2\log k)}\cdot n$, where $k$ is the optimum width and $n$ is the number of vertices. While being slower by a $\log k$-factor in the exponent than the fastest known algorithm, given by Thilikos, Bodlaender, and Serna in [Cutwidth I: A linear time fixed parameter algorithm, J. Algorithms, 56(1):1--24, 2005] and [Cutwidth II: Algorithms for partial $w$-trees of bounded degree, J. Algorithms, 56(1):25--49, 2005], our algorithm has the advantage of being simpler and self-contained; arguably, it explains better the combinatorics of optimum-width layouts

Opinion Dynamics in Online Social Media

Social media have become an important source of information for many of the billions of people who use internet on a regular basis. Pundits and scholars have warned for various adverse effects that its use could have on opinion formation. Personalization algorithms would create filter bubbles—individual information environments in which users become more and more convinced of their own beliefs—and social bots freely spread misinformation to a gullible audience. This dissertation aims to critically evaluate the validity of folk-theories on opinion dynamics in online social media and provide a lens for understanding the ways in which social media platforms shape the process of opinion formation. Using theoretical agent-based computational models and online experiments I investigate three different paths to polarization: the role of personalization algorithms, the strategic use of social bots and the mass dispersion properties of content on social media. First, I find a mismatch between the role of personalization algorithms and state-of-the-art social influence models. Using the information from an experimental study with Facebook users, I predict that personalization of online social media could prevent polarization, particularly when distant groups use different moral foundations of argumentation. Second, the fact that bots stand largely disconnected from human users on social media might make them more, not less effective in spreading their content. Third, the rapid sharing of information to all your contacts at once—typical for information sharing on platforms like Facebook and Twitter—may contribute to isolation of individuals who hold slightly different beliefs

SURFO Technical Report No. 99-4

The 2000 technical reports written by undergraduate students participating in the SURFO (Summer Undergraduate Research Fellowships in Oceanography) Program while at the University of Rhode Island

IONIC BONDING CURRICULUM UNIT: AN ELECTROSTATIC FRAMEWORK

This mixed methods study compared two groups of high school students’ understanding of the ionic bond and the dissolving process. A 5 lesson curriculum unit was developed using Taber’s electrostatic framework (1997) focusing on the electrostatic forces between ions compared to a molecular framework (business-as-usual) and the Next Generation Science Standards (NGSS Lead States, 2013). The lessons were developed to integrate spatially integrated experiences. Experimental (new curriculum unit) and business-as-usual (criss-cross method) students had their spatial skills tested before and after learning about the ionic bond using the Purdue Spatial Visualization-Rotations Test (PVST-Rot; Bodner & Guay, 1997). Students’ content was tested (pre and post) using the Chemical Bonding and Dissociation Diagnostic Assessment (CBDDA; Jang, 2003; Tan & Treagust, 1999; McBroom, 2011). Part of the assessment had two-tiered multiple-choice questions. Another part focused on dissolving of ionic compounds in water (dissociation equations and drawing ionic compounds dissolved in water). This study had one group of students using the new curriculum unit focused on ionic crystals, and the second group used more traditional methods of lab plus lecture. Research Question 1: How does the understanding of the ionic bond and dissolving of ionic compounds in water compare for students using a unit focused on an electrostatic framework to students utilizing a molecular framework (business-as-usual) related to their spatial ability and using the spatial ability as a covariant with treatment group? Research Question 2: How do spatial visualization skills compare for students using an electrostatic framework and students focused on a molecular framework? A model using multiple linear regression was developed for Research Question 1 with the post score for the CBDDA as the dependent variable with pre score on the (CBDDA), Treatment, PVST-Rot Gain (post score minus pre score), and Treatment * PVST-Rot Gain as the independent variables. The null hypothesis was rejected, F(4, 87) = 4.674, p \u3c .05. The model shows statistically evidence that it may predict the score on the post content test. Only the constant and the treatment group were the only statistically significant slopes. Multiple linear regression was used to develop a model using the pre PVST score and the treatment group as the independent variables with the post PVST score as the dependent variable. The null hypothesis was rejected for Research Question 2, F(2,89) = 26.732, p \u3c .05. Only the constant and pre PVST score slope were significant. The qualitative portion of this study utilized the following sources: pre and post student interviews, drawings and dissociation equations from the CBDDA, classroom observations, and teacher logs. Some experimental students were able to improve their dissociation equations and/or the drawings compared to the business-as-usual group. The business-as-usual teacher logs reflected a more molecular framework of teaching. Interviewed students from both groups showed a lack of understanding of the difference between covalent and ionic bonding. Students from both groups did not comprehend that a molecule is used for only covalent compounds. The approximate 3.2 experimental students to one business-as-usual student may be a limitation of this study. The new unit has potential to aid with the understanding of the ionic bond and the dissolving process

Algorithms for Fundamental Problems in Computer Networks.

Traditional studies of algorithms consider the sequential setting, where the whole input data is fed into a single device that computes the solution. Today, the network, such as the Internet, contains of a vast amount of information. The overhead of aggregating all the information into a single device is too expensive, so a distributed approach to solve the problem is often preferable. In this thesis, we aim to develop efficient algorithms for the following fundamental graph problems that arise in networks, in both sequential and distributed settings. Graph coloring is a basic symmetry breaking problem in distributed computing. Each node is to be assigned a color such that adjacent nodes are assigned different colors. Both the efficiency and the quality of coloring are important measures of an algorithm. One of our main contributions is providing tools for obtaining colorings of good quality whose existence are non-trivial. We also consider other optimization problems in the distributed setting. For example, we investigate efficient methods for identifying the connectivity as well as the bottleneck edges in a distributed network. Our approximation algorithm is almost-tight in the sense that the running time matches the known lower bound up to a poly-logarithmic factor. For another example, we model how the task allocation can be done in ant colonies, when the ants may have different capabilities in doing different tasks. The matching problems are one of the classic combinatorial optimization problems. We study the weighted matching problems in the sequential setting. We give a new scaling algorithm for finding the maximum weight perfect matching in general graphs, which improves the long-standing Gabow-Tarjan's algorithm (1991) and matches the running time of the best weighted bipartite perfect matching algorithm (Gabow and Tarjan, 1989). Furthermore, for the maximum weight matching problem in bipartite graphs, we give a faster scaling algorithm whose running time is faster than Gabow and Tarjan's weighted bipartite {it perfect} matching algorithm.PhDComputer Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113540/1/hsinhao_1.pd