Low-Diameter Clusters in Network Analysis

In this dissertation, we introduce several novel tools for cluster-based analysis of complex systems and design solution approaches to solve the corresponding optimization problems. Cluster-based analysis is a subfield of network analysis which utilizes a graph representation of a system to yield meaningful insight into the system structure and functions. Clusters with low diameter are commonly used to characterize cohesive groups in applications for which easy reachability between group members is of high importance. Low-diameter clusters can be mathematically formalized using a clique and an s-club (with relatively small values of s), two concepts from graph theory. A clique is a subset of vertices adjacent to each other and an s-club is a subset of vertices inducing a subgraph with a diameter of at most s. A clique is actually a special case of an s-club with s = 1, hence, having the shortest possible diameter. Two topics of this dissertation focus on graphs prone to uncertainty and disruptions, and introduce several extensions of low-diameter models. First, we introduce a robust clique model in graphs where edges may fail with a certain probability and robustness is enforced using appropriate risk measures. With regard to its ability to capture underlying system uncertainties, finding the largest robust clique is a better alternative to the problem of finding the largest clique. Moreover, it is also a hard combinatorial optimization problem, requiring some effective solution techniques. To this aim, we design several heuristic approaches for detection of large robust cliques and compare their performance. Next, we consider graphs for which uncertainty is not explicitly defined, studying connectivity properties of 2-clubs. We notice that a 2-club can be very vulnerable to disruptions, so we enhance it by reinforcing additional requirements on connectivity and introduce a biconnected 2-club concept. Additionally, we look at the weak 2-club counterpart which we call a fragile 2-club (defined as a 2-club that is not biconnected). The size of the largest biconnected 2-club in a graph can help measure overall system reachability and connectivity, whereas the largest fragile 2-club can identify vulnerable parts of the graph. We show that the problem of finding the largest fragile 2-club is polynomially solvable whereas the problem of finding the largest biconnected 2-club is NP-hard. Furthermore, for the former, we design a polynomial time algorithm and for the latter - combinatorial branch-and-bound and branch-and-cut algorithms. Lastly, we once again consider the s-club concept but shift our focus from finding the largest s-club in a graph to the problem of partitioning the graph into the smallest number of non-overlapping s-clubs. This problem cannot only be applied to derive communities in the graph, but also to reduce the size of the graph and derive its hierarchical structure. The problem of finding the minimum s-club partitioning is a hard combinatorial optimization problem with proven complexity results and is also very hard to solve in practice. We design a branch-and-bound combinatorial optimization algorithm and test it on the problem of minimum 2-club partitioning

Evolution of Ego-networks in Social Media with Link Recommendations

Ego-networks are fundamental structures in social graphs, yet the process of their evolution is still widely unexplored. In an online context, a key question is how link recommender systems may skew the growth of these networks, possibly restraining diversity. To shed light on this matter, we analyze the complete temporal evolution of 170M ego-networks extracted from Flickr and Tumblr, comparing links that are created spontaneously with those that have been algorithmically recommended. We find that the evolution of ego-networks is bursty, community-driven, and characterized by subsequent phases of explosive diameter increase, slight shrinking, and stabilization. Recommendations favor popular and well-connected nodes, limiting the diameter expansion. With a matching experiment aimed at detecting causal relationships from observational data, we find that the bias introduced by the recommendations fosters global diversity in the process of neighbor selection. Last, with two link prediction experiments, we show how insights from our analysis can be used to improve the effectiveness of social recommender systems.Comment: Proceedings of the 10th ACM International Conference on Web Search and Data Mining (WSDM 2017), Cambridge, UK. 10 pages, 16 figures, 1 tabl

Understanding the apparent superiority of over-sampling through an analysis of local information for class-imbalanced data

Data plays a key role in the design of expert and intelligent systems and therefore, data preprocessing appears to be a critical step to produce high-quality data and build accurate machine learning models. Over the past decades, increasing attention has been paid towards the issue of class imbalance and this is now a research hotspot in a variety of fields. Although the resampling methods, either by under-sampling the majority class or by over-sampling the minority class, stand among the most powerful techniques to face this problem, their strengths and weaknesses have typically been discussed based only on the class imbalance ratio. However, several questions remain open and need further exploration. For instance, the subtle differences in performance between the over- and under-sampling algorithms are still under-comprehended, and we hypothesize that they could be better explained by analyzing the inner structure of the data sets. Consequently, this paper attempts to investigate and illustrate the effects of the resampling methods on the inner structure of a data set by exploiting local neighborhood information, identifying the sample types in both classes and analyzing their distribution in each resampled set. Experimental results indicate that the resampling methods that produce the highest proportion of safe samples and the lowest proportion of unsafe samples correspond to those with the highest overall performance. The significance of this paper lies in the fact that our findings may contribute to gain a better understanding of how these techniques perform on class-imbalanced data and why over-sampling has been reported to be usually more efficient than under-sampling. The outcomes in this study may have impact on both research and practice in the design of expert and intelligent systems since a priori knowledge about the internal structure of the imbalanced data sets could be incorporated to the learning algorithms

Expanding Social Network Modeling Software and Agent Models for Diffusion Processes

In an increasingly digitally interconnected world, the study of social networks and their dynamics is burgeoning. Anthropologically, the ubiquity of online social networks has had striking implications for the condition of large portions of humanity. This technology has facilitated content creation of virtually all sorts, information sharing on an unprecedented scale, and connections and communities among people with similar interests and skills. The first part of my research is a social network evolution and visualization engine. Built on top of existing technologies, my software is designed to provide abstractions from the underlying libraries, drive real-time network evolution based on user-defined parameters, and optionally visualize that evolution at each step of the process. My software provides a low maintenance interface for the creation of networks and update schemes for a wide array of experimental contexts, an engine to drive network evolution, and a visualization platform to provide real-time feedback about different aspects of the network to the researcher, as well as fine-grained debugging tools. We conducted investigations into the opinion dynamics of networks when multiple agent “archetypes” interact together with this platform. We modeled agents’ archetypes with respect to two attributes: their preference over their friends’ opinion profiles, and their tendency to change their opinion over time. We extended the current state of agent modeling in opinion diffusion by providing a unified 2D trajectory/preference space for agents that incorporates most common models in the literature. We investigated six agent archetypes from this space, and examined the behavior of the network as a whole and the individual agents in a variety of contexts. In another branch of work using our software, we developed a network of agents who must carry out both economic and social activities during a pandemic. Agents’ decisions about what actions to take (self-protective measures like masking, social distancing, or waiting to run errands) are based on several factors, including perception of risk (obtained from news reports, social connections, etc.) and economic need. We show with preliminary testing that this platform is able to execute standard pandemic models successfully with the incorporation of the economic and social dimensions, and that this paradigm may provide useful insight into effective agent-level response policies that can be used in concert with other top-down approaches that comprise most of the recent pandemic response research. We have investigated the implications of varying behavior profiles within a network of agents, and how those behavioral compositions affect the overall climate of the network in return, and this software will continue to facilitate similar research into the future

Blood Vessel Tortuosity Selects against Evolution of Agressive Tumor Cells in Confined Tissue Environments: a Modeling Approach

Cancer is a disease of cellular regulation, often initiated by genetic mutation within cells, and leading to a heterogeneous cell population within tissues. In the competition for nutrients and growth space within the tumors the phenotype of each cell determines its success. Selection in this process is imposed by both the microenvironment (neighboring cells, extracellular matrix, and diffusing substances), and the whole of the organism through for example the blood supply. In this view, the development of tumor cells is in close interaction with their increasingly changing environment: the more cells can change, the more their environment will change. Furthermore, instabilities are also introduced on the organism level: blood supply can be blocked by increased tissue pressure or the tortuosity of the tumor-neovascular vessels. This coupling between cell, microenvironment, and organism results in behavior that is hard to predict. Here we introduce a cell-based computational model to study the effect of blood flow obstruction on the micro-evolution of cells within a cancerous tissue. We demonstrate that stages of tumor development emerge naturally, without the need for sequential mutation of specific genes. Secondly, we show that instabilities in blood supply can impact the overall development of tumors and lead to the extinction of the dominant aggressive phenotype, showing a clear distinction between the fitness at the cell level and survival of the population. This provides new insights into potential side effects of recent tumor vasculature renormalization approaches

Evolutionary games on graphs

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.Comment: Review, final version, 133 pages, 65 figure

Event program

UNLV Undergraduates from all departments, programs and colleges participated in a campus-wide symposium on April 16, 2011. Undergraduate posters from all disciplines and also oral presentations of research activities, readings and other creative endeavors were exhibited throughout the festival