TRP (Transient Receptor Potential) cation channels of the TRPM subfamily have been found to be critically important for the regulation of Mg2+ homeostasis in both protostomes (e.g., the nematode, C. elegans, and the insect, D. melanogaster) and deuterostomes (e.g., humans). Although significant progress has been made toward understanding how the activities of these channels are regulated, there...

Let n ∈ N \ {0, 1, 2}. We prove that there exists up to equivalence one and up to isomorphism (n + 1)(2n + 1) isometric embeddings of the near 2n-gon Hn into the near 2n-gon Gn.

A 33-year-old man presented with a nine-month history of severe, refractory unilateral occipital neuralgia. The diagnosis was made based on the International Classification for Headache Disorders (ICHD-II) criteria for occipital neuralgia, including paroxysmal stabbing pain with persistent aching between paroxysms in the distributions of the greater occipital nerve (GON), tenderness over the af...

Definition 3 (Polygonal Triangulation). Let K be a two-dimensional simplicial complex (i.e., a collection of triangles). If K is homeomorphic to a disk, then it is called a triangulation of a disk. Furthermore, if K is a k-gon divided by diagonals into k − 2 triangles, then K will be called a polygonal triangulation. See Figure 1. A k-gon dissected into k − 2 triangles will be called a k-triang...

In 1935, Paul Erdős and George Szekeres were able to show that any point set large enough contains the vertices of a convex k-gon. Later in 1961, they constructed a point set of size 2k−2 not containing the vertex set of any convex k-gon. This leads to what is known as the Erdős-Szekeres Conjecture, that any point set of 2k−2 + 1 points contains the vertices of a convex k-gon. Recently, this fa...

International Computer Science Institute, Berkeley, CA 2007 – Present Postdoctoral Researcher, Networking Group, working with Prof. Scott Shenker, Dr. Petros Maniatis, and Dr. Sylvia Ratnasamy Diverse replication for single-machine Byzantine-fault tolerance: Investigate exploiting cores in many-core systems to defend against software attacks. Explore different isolation and software diversity m...

We consider polygon and simplex equations, of which the simplest nontrivial examples are pentagon (5-gon) Yang–Baxter (2-simplex), respectively. examine general structure (2n + 1)-gon 2n-simplex equations in direct sums vector spaces. Then, we provide a construction for their solutions, parameterized by elements Grassmannian Gr(n 1, 2n 1).

We introduce the sequence of generalized Gon£arov polynomials, which is a basis for the solutions to the Gon£arov interpolation problem with respect to a delta operator. Explicitly, a generalized Gon£arov basis is a sequence (tn(x))n≥0 of polynomials de ned by the biorthogonality relation εzi(d (tn(x))) = n!δi,n for all i, n ∈ N, where d is a delta operator, Z = (zi)i≥0 a sequence of scalars, a...

Patients with primary headaches often report pain that involves not only the front of the head, innervated by the first (ophthalmic) division of the trigeminal nerve, but also the back of the head, innervated by the greater occipital nerve (GON) that is a branch of the C(2) spinal root. The aim of this work was to study the physiology of trigeminocervical input in a model of cranial nociception...