Heesung Shin

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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 = 1e2e . . . of a tree on the vertex(More)
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 contexts.(More)
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)
A leader of a tree T on [n] is a vertex which has no smaller descendants in T . Gessel and Seo showed that ∑ T ∈Tn u(# of leaders in T )c(degree of 1 in T ) = uPn−1(1, u, cu), which is a generalization of Cayley’s 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 the Prüfer code which is called(More)
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)
For a fixed sequence of n positive integers (a, b̄) := (a, b, b, . . . , b), an (a, b̄)-parking function of length n is a sequence (p1, p2, . . . , pn) of positive integers whose nondecreasing rearrangement q1 ≤ q2 ≤ · · · ≤ qn satisfies qi ≤ a + (i − 1)b for any i = 1, . . . , n. A (a, b̄)-forest on n-set is a rooted vertex-colored forests on n-set whose(More)
André proved that the number of alternating permutations on {1, 2, ..., n} is equal to the Euler number En. A refinement of André’s result was given by Entringer, who proved that counting alternating permutations according to the first element gives rise to Seidel’s triangle (En,k) for computing the Euler numbers. In a series of papers, using generating(More)