Browsing by Author "Lam, Thomas"

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    From dimers to webs
    (AMS, 2019) Fraser, Chris; Lam, Thomas; Le, Ian; Mathematical Sciences, School of Science
    We formulate a higher-rank version of the boundary measurement map for weighted planar bipartite networks in the disk. It sends a network to a linear combination of $ \textnormal {SL}_r$-webs and is built upon the $ r$-fold dimer model on the network. When $ r$ equals 1, our map is a reformulation of Postnikov's boundary measurement used to coordinatize positroid strata. When $ r$ equals 2 or 3, it is a reformulation of the $ \textnormal {SL}_2$- and $ \textnormal {SL}_3$-web immanants defined by the second author. The basic result is that the higher-rank map factors through Postnikov's map. As an application, we deduce generators and relations for the space of $ \textnormal {SL}_r$-webs, re-proving a result of Cautis-Kamnitzer-Morrison. We establish compatibility between our map and restriction to positroid strata and thus between webs and total positivity.
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    The Reverse Galeal Hinge Flap: Another Valuable Technique in the Repair of Scalp Defects Extending to the Calvarium
    (Lippincott Williams & Wilkins, 2015-04) Lam, Thomas; Miletta, Nathanial R.; Bingham, Jonathan L.; Department of Dermatology, IU School of Medicine
    Over the last 30 years, the estimated incidence of nonmelanoma skin cancer (NMSC) has increased from 300,000 to greater than 2 million cases. Approximately 15% of these cancers occur on the scalp.1 Given the increasing incidence of NMSC and their predilection for the scalp, the demand for scalp repairs will continue to rise. It is important that the dermatologic surgeon is equipped to manage these cases, in particular defects that extend to the bone.The repair of large scalp defects extending to the calvarium is especially challenging for several reasons. The primary closure of any large scalp wound is complicated by the relative inelasticity of scalp tissue and the convexity of the scalp. Rotation flaps are the mainstay technique of re-approximating large scalp wounds but are often unable to completely close very large defects.2 Skin grafts can also be used to cover wounds primarily or in conjunction with other closure techniques.2 However, when scalp defects extend to the bone, the poor vascularity of the osseous tissue severely limits both skin grafting and xenografting. Various approaches to making exposed bone more suitable for grafting have been described in the recent literature, and these techniques and their limitations will be briefly discussed.3–5 The authors will also present two cases that outline a simple method of re-establishing a vascular bed on exposed bone using a reverse galeal hinge flap.