Sense-making in theory and practice: a metatheoretical foundation and application for health information seeking

This thesis attempts to provide deeper historical and theoretical grounding for sense-making, thereby illustrating its applicability to practical information seeking research. In Chapter One I trace the philosophical origins of Brenda Dervin’s theory known as “sense making,” reaching beyond current scholarship that locates the origins of sense-making in twentieth-century Phenomenology and Communication theory and find its rich ontological, epistemological, and etymological heritage that dates back to the Pre-Socratics. After exploring sense-making’s Greek roots, I examine sense-making’s philosophical undercurrents found in Hegel’s Phenomenology of Spirit (1807), where he also returns to the simplicity of the Greeks for his concept of sense. With Chapter Two I explore sense-making methodology and find, in light of the Greek and Hegelian dialectic, a dialogical bridge connecting sense-making’s theory with pragmatic uses. This bridge between Dervin’s situation and use occupies a distinct position in sense-making theory. Moreover, building upon Brenda Dervin’s model of sense-making, I use her metaphors of gap and bridge analogy to discuss the dialectic and dialogic components of sense making. The purpose of Chapter Three is pragmatic – to gain insight into the online information-seeking needs, experiences, and motivation of first-degree relatives (FDRs) of breast cancer survivors through the lens of sense-making. This research analyses four questions: 1) information-seeking behavior among FDRs of cancer survivors compared to survivors and to undiagnosed, non-related online cancer information seekers in the general population, 2) types of and places where information is sought, 3) barriers or gaps and satisfaction rates FDRs face in their cancer information quest, and 4) types and degrees of cancer information and resources FDRs want and use in their information search for themselves and other family members. An online survey instrument designed to investigate these questions was developed and pilot tested. Via an email communication, the Susan Love Breast Cancer Research Foundation distributed 322,000 invitations to its membership to complete the survey, and from March 24th to April 5th 10,692 women agreed to take the survey with 8,804 volunteers actually completing survey responses. Of the 8,804 surveys, 95% of FDRs have searched for cancer information online, and 84% of FDRs use the Internet as a sense-making tool for additional information they have received from doctors or nurses. FDRs report needing much more information than either survivors or family/friends in ten out of fifteen categories related to breast and ovarian cancer. When searching for cancer information online, FDRs also rank highest in several of sense-making’s emotional levels: uncertainty, confusion, frustration, doubt, and disappointment than do either survivors or friends and family. The sense-making process has existed in theory and praxis since the early Greeks. In applying sense–making’s theory to a contemporary problem, the survey reveals unaddressed situations and gaps of FDRs’ information search process. FDRs are a highly motivated group of online information seekers whose needs are largely unaddressed as a result of gaps in available online information targeted to address their specific needs. Since FDRs represent a quarter of the population, further research addressing their specific online information needs and experiences is necessary.

Approximation Algorithms for Network Design and Orienteering

This thesis presents approximation algorithms for some NP-Hard combinatorial optimization problems on graphs and networks; in particular, we study problems related to Network Design. Under the widely-believed complexity-theoretic assumption that P is not equal to NP, there are no efficient (i.e., polynomial-time) algorithms that solve these problems exactly. Hence, if one desires efficient algorithms for such problems, it is necessary to consider approximate solutions: An approximation algorithm for an NP-Hard problem is a polynomial time algorithm which, for any instance of the problem, finds a solution whose value is guaranteed to be within a multiplicative factor of the value of an optimal solution to that instance. We attempt to design algorithms for which this factor, referred to as the approximation ratio of the algorithm, is as small as possible. The field of Network Design comprises a large class of problems that deal with constructing networks of low cost and/or high capacity, routing data through existing networks, and many related issues. In this thesis, we focus chiefly on designing fault-tolerant networks. Two vertices u,v in a network are said to be k-edge-connected if deleting any set of k − 1 edges leaves u and v connected; similarly, they are k-vertex connected if deleting any set of k − 1 other vertices or edges leaves u and v connected. We focus on building networks that are highly connected, meaning that even if a small number of edges and nodes fail, the remaining nodes will still be able to communicate. A brief description of some of our results is given below. We study the problem of building 2-vertex-connected networks that are large and have low cost. Given an n-node graph with costs on its edges and any integer k, we give an O(log n log k) approximation for the problem of finding a minimum-cost 2-vertex-connected subgraph containing at least k nodes. We also give an algorithm of similar approximation ratio for maximizing the number of nodes in a 2-vertex-connected subgraph subject to a budget constraint on the total cost of its edges. Our algorithms are based on a pruning process that, given a 2-vertex-connected graph, finds a 2-vertex-connected subgraph of any desired size and of density comparable to the input graph, where the density of a graph is the ratio of its cost to the number of vertices it contains. This pruning algorithm is simple and efficient, and is likely to find additional applications. Recent breakthroughs on vertex-connectivity have made use of algorithms for element-connectivity problems. We develop an algorithm that, given a graph with some vertices marked as terminals, significantly simplifies the graph while preserving the pairwise element-connectivity of all terminals; in fact, the resulting graph is bipartite. We believe that our simplification/reduction algorithm will be a useful tool in many settings. We illustrate its applicability by giving algorithms to find many trees that each span a given terminal set, while being disjoint on edges and non-terminal vertices; such problems have applications in VLSI design and other areas. We also use this reduction algorithm to analyze simple algorithms for single-sink network design problems with high vertex-connectivity requirements; we give an O(k log n)-approximation for the problem of k-connecting a given set of terminals to a common sink. We study similar problems in which different types of links, of varying capacities and costs, can be used to connect nodes; assuming there are economies of scale, we give algorithms to construct low-cost networks with sufficient capacity or bandwidth to simultaneously support flow from each terminal to the common sink along many vertex-disjoint paths. We further investigate capacitated network design, where edges may have arbitrary costs and capacities. Given a connectivity requirement R_uv for each pair of vertices u,v, the goal is to find a low-cost network which, for each uv, can support a flow of R_uv units of traffic between u and v. We study several special cases of this problem, giving both algorithmic and hardness results. In addition to Network Design, we consider certain Traveling Salesperson-like problems, where the goal is to find short walks that visit many distinct vertices. We give a (2 + epsilon)-approximation for Orienteering in undirected graphs, achieving the best known approximation ratio, and the first approximation algorithm for Orienteering in directed graphs. We also give improved algorithms for Orienteering with time windows, in which vertices must be visited between specified release times and deadlines, and other related problems. These problems are motivated by applications in the fields of vehicle routing, delivery and transportation of goods, and robot path planning.

Problems in number theory and hyperbolic geometry

In the first part of this thesis we generalize a theorem of Kiming and Olsson concerning the existence of Ramanujan-type congruences for a class of eta quotients. Specifically, we consider a class of generating functions analogous to the generating function of the partition function and establish a bound on the primes ℓ for which their coefficients c(n) obey congruences of the form c(ℓn + a) ≡ 0 (mod ℓ). We use this last result to answer a question of H.C. Chan. In the second part of this thesis [S2] we explore a natural analog of D. Calegari’s result that there are no hyperbolic once-punctured torus bundles over S^1 with trace field having a real place. We prove a contrasting theorem showing the existence of several infinite families of pairs (−χ, p) such that there exist hyperbolic surface bundles over S^1 with trace field of having a real place and with fiber having p punctures and Euler characteristic χ. This supports our conjecture that with finitely many known exceptions there exist such examples for each pair ( −χ, p).