Efficient Structures for Innovative Social Networks

What lines of communication among members of an organization are most effective in the early, ideation phase of innovation? We investigate this question with a recombination and selection model of knowledge transfer operating through a social network. We measure cost in human time, and seek efficient social network structures in the time--total cost plane (minimize ideation time subject to an upper bound on total cost, or vice versa) and in the time--cost per period plane, with a similar interpretation. Our results suggest that efficiently innovative organizations look nothing like what one intuitively associates with standard formal organizations with strict and unchanging lines of communication, nor do they conform with what one might expect from static social network representations of communication patterns. Rather, ideation is accelerated when people dynamically churn through a large (ideally the entire population) set of conversational partners over time, which naturally begets short path lengths and eliminates information bottlenecks. In organizations with these features group meetings do not help and can hurt the process, because many parallel conversations can achieve the same or better results as one-to-many communications. A family of networks called the complete wheel-stars emerges as an important family on the time-cost efficient frontier. Wheel-star graphs have a completely connected clique of agents at the center, with all other agents connected to the core but not to each other; the star and the complete graph are its extreme elements. We discuss the consequences of these results for organizations and sociometric analyses.http://deepblue.lib.umich.edu/bitstream/2027.42/64992/1/1136_lovejoy.pd

A Local Perspective on the Edge Removal Problem

The edge removal problem studies the loss in network coding rates that results when a network communication edge is removed from a given network. It is known, for example, that in networks restricted to linear coding schemes and networks restricted to Abelian group codes, removing an edge e^∗ with capacity R_(e^∗) reduces the achievable rate on each source by no more than R_(e^∗). In this work, we seek to uncover larger families of encoding functions for which the edge removal statement holds. We take a local perspective: instead of requiring that all network encoding functions satisfy certain restrictions (e.g., linearity), we limit only the function carried on the removed edge e^∗. Our central results give sufficient conditions on the function carried by edge e^∗ in the code used to achieve a particular rate vector under which we can demonstrate the achievability of a related rate vector once e^∗ is removed

Self-Revelation in The Scarlet Letter

Paper by J. A. War

A version of Tutte's polynomial for hypergraphs

Tutte's dichromate T(x,y) is a well known graph invariant. Using the original definition in terms of internal and external activities as our point of departure, we generalize the valuations T(x,1) and T(1,y) to hypergraphs. In the definition, we associate activities to hypertrees, which are generalizations of the indicator function of the edge set of a spanning tree. We prove that hypertrees form a lattice polytope which is the set of bases in a polymatroid. In fact, we extend our invariants to integer polymatroids as well. We also examine hypergraphs that can be represented by planar bipartite graphs, write their hypertree polytopes in the form of a determinant, and prove a duality property that leads to an extension of Tutte's Tree Trinity Theorem.Comment: 49 page

Gender, place, and cultural memory: intersections of American national identity and the art of Hopi-Choctaw Linda Lomahaftewa

M.A. in Art History, University of Oklahoma, 2014.Includes bibliographical references.Overlooked in the mainstream of so-called American Art, the work of Hopi-Choctaw Linda Lomahaftewa embodies significant aspects of United States history. Despite a prolific oeuvre centered in a place-based aesthetic that recalls cultural memories from an "indigenous feminine" perspective, and a narrative that connects with significant people and moments from history, little scholarly attention has been paid to this remarkable woman. Further, there remains an absence of recognition for Lomahaftewa's art in major American Art museums. In this thesis, I suggest that Lomahaftewa's absence from these institutions of embodied knowledges speaks to a specific agenda - and subsequent hegemonic system - begun at contact by the western patriarchy. By looking at her life and work through the lens of feminist theory, I resist normative assumptions of aesthetics when I argue for the presence of Lomahaftewa's art in the mainstream American Art museum