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A combinatorial bijection between k-edge colored trees and colored Prüfer codes for labelled trees is established. This bijection gives a simple combinatorial proof for the number k(n − 2)! nk−n n−2 of k-edge colored trees with n vertices.

For a labeled tree on the vertex set {1, 2,. .. , n}, the local direction of each edge (i j) is from i to j if i < j. For a rooted tree, there is also a natural global direction of edges towards the root. The number of edges pointing to a vertex is called its indegree. Thus the local (resp. global) indegree sequence λ = 1 e1 2 e2. .. of a tree on the vertex… (More)

BACKGROUND
Cells coordinate their metabolism, proliferation, and cellular communication according to environmental cues through signal transduction. Because signal transduction has a primary role in cellular processes, many experimental techniques and approaches have emerged to discover the molecular components and dynamics that are dependent on cellular… (More)

A leader of a tree T on [n] is a vertex which has no smaller descendants in T. Gessel and Seo showed T ∈Tn u (# of leaders in T) c (degree of 1 in T) = u Pn−1(1, u, cu), which is a generalization of Cayley formula, where Tn is the set of trees on [n] and Pn(a, b, c) = c n−1 i=1 (ia + (n − i)b + c). Using a variation of Prüfer code which is called a RP-code,… (More)

- Jung-Yoon Yoo, Heesung Shin, Tae Hoon Kim, Won-Seok Choi, Susan D. Ferguson, Asgerally T. Fazleabas +4 others
- PloS one
- 2014

Endometriosis, defined as the presence of endometrial cells outside of the uterine cavity, is a major cause of infertility and pelvic pain, afflicting more than 10% of reproductive age women. Endometriosis is a chronic inflammatory disease and lipopolysaccharide promotes the proliferation and invasion of endometriotic stromal cells. Cysteine-rich secretory… (More)

- Jung-Hoon Lee, Heesung Shin, Yong-Jae Kim, Se-Hwan Paek, Shouguang Jin, Un-Hwan Ha
- Journal of Microbiology
- 2014

The proinflammatory cytokine interleukin-1β plays an important role in protecting the host against airway infection; however, it can also trigger a massive influx of neutrophils into the airways, causing tissue damage. Anti-inflammatory treatments are particularly in demand for patients suffering from chronic inflammatory diseases. Sophora flavescens is a… (More)