Diameter and Rumour Spreading in Real-World Network Models

The so-called 'small-world phenomenon', observed in many real-world networks, is that there is a short path between any two nodes of a network, whose length is much smaller that the network's size, typically growing as a logarithmic function. Several mathematical models have been defined for social networks, the WWW, etc., and this phenomenon translates to proving that such models have a small diameter. In the first part of this thesis, we rigorously analyze the diameters of several random graph classes that are introduced specifically to model complex networks, verifying whether this phenomenon occurs in them. In Chapter 3 we develop a versatile technique for proving upper bounds for diameters of evolving random graph models, which is based on defining a coupling between these models and variants of random recursive trees. Using this technique we prove, for the first time, logarithmic upper bounds for the diameters of seven well known models. This technique gives unified simple proofs for known results, provides lots of new ones, and will help in proving many of the forthcoming network models are small-world. Perhaps, for any given model, one can come up with an ad hoc argument that the diameter is O(log n), but it is interesting that a unified technique works for such a wide variety of models, and our first major contribution is introducing such a technique. In Chapter 4 we estimate the diameter of random Apollonian networks, a class of random planar graphs. We also give lower and upper bounds for the length of their longest paths. In Chapter 5 we study the diameter of another random graph model, called the random surfer Web-graph model. We find logarithmic upper bounds for the diameter, which are almost tight in the special case when the growing graph is a tree. Although the two models are quite different, surprisingly the same engine is used for proving these results, namely the powerful technique of Broutin and Devroye (Large deviations for the weighted height of an extended class of trees, Algorithmica 2006) for analyzing weighted heights of random trees, which we have adapted and applied to the two random graph models. Our second major contribution is demonstrating the flexibility of this technique via providing two significant applications. In the second part of the thesis, we study rumour spreading in networks. Suppose that initially a node has a piece of information and wants to spread it to all nodes in a network quickly. The problem of designing an efficient protocol performing this task is a fundamental one in distributed computing and has applications in maintenance of replicated databases, broadcasting algorithms, analyzing news propagation is social networks and the spread of viruses on the Internet. Given a rumour spreading protocol, its spread time is the time it takes for the rumour to spread in the whole graph. In Chapter 6 we prove several tight lower and upper bounds for the spread times of two well known randomized rumour spreading protocols, namely the synchronous push&pull protocol and the asynchronous push&pull protocol. In particular, we show the average spread time in both protocols is always at most linear. In Chapter 7 we study the performance of the synchronous push&pull protocol on random k-trees. We show that a.a.s. after a polylogarithmic amount of time, 99 percent of the nodes are informed, but to inform all vertices, a polynomial amount of time is required. Our third majoc contribution is giving analytical proofs for two experimentally verified statements: firstly, the asynchronous push&pull protocol is typically faster than its synchronous variant, and secondly, it takes considerably more time to inform the last 1 percent of the vertices in a social network than the first 99 percent. We hope that our work on the asynchronous push&pull protocol attracts attention to this fascinating model

Critical phenomena in complex networks

The combination of the compactness of networks, featuring small diameters, and their complex architectures results in a variety of critical effects dramatically different from those in cooperative systems on lattices. In the last few years, researchers have made important steps toward understanding the qualitatively new critical phenomena in complex networks. We review the results, concepts, and methods of this rapidly developing field. Here we mostly consider two closely related classes of these critical phenomena, namely structural phase transitions in the network architectures and transitions in cooperative models on networks as substrates. We also discuss systems where a network and interacting agents on it influence each other. We overview a wide range of critical phenomena in equilibrium and growing networks including the birth of the giant connected component, percolation, k-core percolation, phenomena near epidemic thresholds, condensation transitions, critical phenomena in spin models placed on networks, synchronization, and self-organized criticality effects in interacting systems on networks. We also discuss strong finite size effects in these systems and highlight open problems and perspectives.Comment: Review article, 79 pages, 43 figures, 1 table, 508 references, extende

Modern Time: Photography and Temporality

This dissertation explores the fluid relationship of photography to time. Many theorists have noted that photography has a distinctive manner of representing temporality. Roland Barthes, for example, wrote that the photograph has a peculiar capacity to represent the past in the present, and thus to imply the passing of time in general. As a consequence, Barthes argued, all photographs speak of the inevitability of our own death in the future. Moreover, he linked photography\u27s peculiar temporality to its capacity for a certain kind of realism: false on the level of perception, true on the level of time. Barthes\u27s analysis poses a challenge to all commentators on photography - what exactly is photography\u27s relationship to time, and by extension, to reality? This dissertation addresses that two-part question by analyzing in detail a sample of understudied vernacular photographic practices. Rather than provide a comprehensive, and necessarily incomplete, study of every possible way in which photography can relate to time, this study instead focuses on a number of in-depth analyses of specific photographic practices. These practices represent time in at least three distinct ways: as narrative time, device-altered time, and composite time. My study examines the motivations for photography\u27s insistent struggle to reorganize time\u27s passage, to freeze or slow it for a moment, or to give form to time\u27s fluctuating conditions. I suggest that this struggle is both symptomatic of modernity as a general phenomenon and a manifestation of the photographic medium\u27s conditional relationship to reality, a relationship which arguably has been complicated by the use of digital technology. This dissertation examines photography\u27s unique capacity to represent the passage of time with a degree of elasticity, simultaneity, and abstraction. The medium\u27s ability to represent many levels of temporal experience and indexical slippage, I argue, illustrates photography\u27s potential to relate to and reflect the complexities of modern consciousness. This dissertation also exemplifies the need for a new kind of history - one that addresses the multiple identities of the photographic rather than simply the photograph. This work is a contribution to that project

Authorship and Strategies of Representation in the Fiction of A. S. Byatt

This thesis examines the portrayal of authorship in Byatt’s novels with a particular focus on her use of character-authors as a site for the destabilisation of dominant literary and cultural paradigms. Byatt has been perceived as a liberal-humanist author, ambivalent to postmodern, post-structuralist and feminist literary theory. Whilst Byatt’s frame narratives are realist and align with liberal-humanist values, she employs many different genres in the embedded texts written by her character-authors, including fairy-tale, life-writing and historical drama. The diverse representational practices in the novels construct a metafictional commentary on realism, undermining its conventions and conservative politics. My analysis focuses on the relationship between the embedded texts and the frame narrative to demonstrate that Byatt’s strategies of representation enact a postmodern complicitous critique of literary conventions and grand narratives. Many of the female protagonists and minor characters are authors, in the broad sense of cultural production, and Byatt uses their engagement with representation of women in literature to pose questions about how cultural narratives naturalise patriarchal definitions of femininity. That Byatt’s female characters resist patriarchal power relations by undermining the cultural script of conventional femininity has been under-explored and consequently critics have overlooked significant instances of female agency. Whilst some branches of postmodern and feminism literary theory have conceptualised agency differently, this thesis emphasises their shared analysis of the discursive construction of subjectivity, as it illuminates Byatt’s disruption of literary conventions. My focus on the embedded texts and the discursive construction of authorship in Byatt’s fiction enables me to address the numerous paradoxes and inconsistencies in the novels as fertile sites that undermine Byatt’s presumed politics

Annual Report of the University, 2000-2001, Volumes 1-4

Message from the President Thank you for joining me in this look back over the past year at the University of New Mexico. It was a year filled with activity, accomplishment and challenge, and this is our opportunity to reflect back on that year. In 2000-2001 we engaged in a University-wide strategic planning process that called on the energies and talents of hundreds of individuals- faculty, staff, students and members of our broader community. The plan, which will be completed in Fall 2001, will serve as our roadmap for the future and will guide our efforts to capitalize on the opportunities and to meet the challenges of the next several years. This process has encouraged us to examine closely our mission and our values, who we are and what we aspire to become. It has given us reason to be proud of our past and cause to think seriously about how we must change in the future. While this was a year for looking ahead, it was also a year of significant accomplishment. For example, we launched a comprehensive set of programs designed to enrich the academic and social experiences of our undergraduate students. We began the implementation of Freshman Learning Communities where small cohorts of students study and learn together in a common set of courses under the guidance of a senior faculty scholar. We reorganized our advisement systems, we undertook the construction or renovation of student-centered facilities on campus, and we created new support systems to enhance student academic success. It was a year in which our support of faculty, staff and students was our highest priority. Through the support of the New Mexico Legislature, faculty and staff received significant salary increases. A new health benefits plan for graduate assistants was implemented. Our Staff as Students program enabled more than 40 staff members to obtain UNM degrees. And, a Center for Scholarship in Teaching and Learning was established to assist faculty in their efforts to develop more effective teaching skills. Finally, this was a year in which UNM dramatically expanded its role in the local community and throughout the state. Never before has the University been as active or as visible in meeting its public responsibility as it was in 2000-2001. From its active participation in economic development initiatives, to its involvement in K-12 educational improvement efforts, to its significant leadership role in health care delivery, UNM demonstrated its ability to help the state meet its most pressing social challenges. And, as UNM took on a more visible role in supporting the state\\u27s citizens, the support for UNM was returned in kind. This year, annual giving to the University rose to a record 35.3 million dollars, a 40% increase over just two years ago. All told, it has been a gratifying and successful year. However, we cannot allow our past accomplishments to mask the continued challenges facing this University. Neither will we allow these challenges to dominate our thinking and diminish out pride in what the University has achieved. So we will savor our successes and continue to move forward. As always, we thank you for sharing our dreams and for supporting the University of New Mexico. Sincerely, William C. Gordon, Presiden

Animating Film Theory

Animating Film Theory provides an enriched understanding of the relationship between two of the most unwieldy and unstable organizing concepts in cinema and media studies: animation and film theory. For the most part, animation has been excluded from the purview of film theory. The contributors to this collection consider the reasons for this marginalization while also bringing attention to key historical contributions across a wide range of animation practices, geographic and linguistic terrains, and historical periods. They delve deep into questions of how animation might best be understood, as well as how it relates to concepts such as the still, the moving image, the frame, animism, and utopia. The contributors take on the kinds of theoretical questions that have remained underexplored because, as Karen Beckman argues, scholars of cinema and media studies have allowed themselves to be constrained by too narrow a sense of what cinema is. This collection reanimates and expands film studies by taking the concept of animation seriously. Contributors. Karen Beckman, Suzanne Buchan, Scott Bukatman, Alan Cholodenko, Yuriko Furuhata, Alexander R. Galloway, Oliver Gaycken, Bishnupriya Ghosh, Tom Gunning, Andrew R. Johnston, Hervé Joubert-Laurencin, Gertrud Koch, Thomas LaMarre, Christopher P. Lehman, Esther Leslie, John MacKay, Mihaela Mihailova, Marc Steinberg, Tess Takahash

Christianity, Islam, and Oriṣa Religion: Three Traditions in Comparison and Interaction

"The Yoruba of southwestern Nigeria are exceptional for the copresence among them of three religious traditions: Islam, Christianity, and the indigenous oriṣa religion. In this comparative study, at once historical and anthropological, Peel explores the intertwined character of the three religions and the dense imbrication of religion in all aspects of Yoruba history up to the present. For over 400 years, the Yoruba have straddled two geocultural spheres: one reaching north over the Sahara to the world of Islam, the other linking them to the Euro-American world via the Atlantic. These two external spheres were the source of contrasting cultural influences, notably those emanating from the world religions. However, the Yoruba not only imported Islam and Christianity but also exported their own oriṣa religion to the New World. Before the voluntary modern diaspora that has brought many Yoruba to Europe and the Americas, tens of thousands were sold as slaves in the New World, bringing with them the worship of the oriṣa. Peel offers deep insight into important contemporary themes such as religious conversion, new religious movements, relations between world religions, the conditions of religious violence, the transnational flows of contemporary religion, and the interplay between tradition and the demands of an ever-changing present. In the process, he makes a major theoretical contribution to the anthropology of world religions.