We initiate the study of approximating the largest induced expander in a given graph G. Given a ∆-regular graph G with n vertices, the goal is to find the set with the largest induced expansion of size at least δ ·n. We design a bi-criteria approximation algorithm for this problem; if the optimum has induced spectral expansion λ our algorithm returns a λ log δ exp(∆/λ) -(spectral) expander of s...

RME was invented by Emerson Angell in 1860.1Angell EH. Treatment of irregularity the permanent or adult teeth.Dental Cosmos. 1860; 1 (599-600): 540-544Google Scholar His case report published Dental Cosmos, first national journal for dental profession. Angell's patient a 14-year-old girl fitted with transpalatal appliance that featured two counter-rotating screws. After weeks turning screws on ...

Let G = (V,E) be an undirected d-regular graph, here, |V | = n, deg(u) = d for all u ∈ V . We will typically interpret the properties of expander graphs in an asymptotic sense. That is, there will be an infinite family of graphs G, with a growing number of vertices n. By “sparse”, we mean that the degree d of G should be very slowly growing as a function of n. When n goes to infinity (n → ∞), d...

The expander constructions based on algebraic methods can give expanders that are both explicit (i.e. we can quickly construct the graph, or even obtain neighborhood information without constructing the entire graph, and Ramanujan, meaning that the spectral gap is essentially as large as possible. It also follows from this spectral bound that the edge expansion of Ramanujan graphs is essentiall...

1. Schulman MR, Chun JK. The conjoined sternalispectoralis muscle flap in immediate tissue expander reconstruction after mastectomy. Ann Plast Surg 2005;55:672-5. 2. Barlow RN. The sternalis muscle in American whites and Negroes. Anat Rec 1934;61:416-26. 3. Alani HA, Balalaa N. Complete tissue expander coverage by musculo-fascial flaps in immediate breast mound reconstruction after mastectomy. ...

Sarday, O cber 7, 2017 the expander. Radiation oncologists and medical physicists will need to consider what effect the gas filled chamber and metal components within the expander have on their treatment planning and dosimetry. Breast air expanders require a wedged pair planning technique however, Saline expanders can be planned with a IMRT hybrid technique. It is critical to understand the con...

Since its application to the NGL process in 1964, the turbo-expander based demethanizer process has been the workhorse of many gas plants. The turbo-expander process isentropically expands the gas through a high speed turbine to create cryogenic temperatures facilitating the separation of ethane and heavier components from the methane. This process also uses significant heat integration to redu...