S. Alex Rautu

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We study the leaf-to-leaf distances on one-dimensionally ordered, full and complete m-ary tree graphs using a recursive approach. In our formulation, unlike in traditional graph theory approaches, leaves are ordered along a line emulating a one-dimensional lattice. We find explicit analytical formulas for the sum of all paths for arbitrary leaf separation r(More)
We study the average leaf-to-leaf path lengths on ordered Catalan tree graphs with n nodes and show that these are equivalent to the average length of paths starting from the root node. We give an explicit analytic formula for the average leaf-to-leaf path length as a function of separation of the leaves and study its asymptotic properties. At the heart of(More)
We study the effect of membrane proteins on the shape, composition and thermodynamic stability of the surrounding membrane. When the coupling between membrane composition and curvature is strong enough the nearby composition and shape both undergo a transition from over-damped to under-damped spatial variation, well before the membrane becomes unstable in(More)
The mechanical properties of phospholipid membranes have been extensively studied over the past few decades [1]. Their ability to bend under very low stress is one of the main mechanical properties of such soft materials. This softness is characterized by a very small value of the bending modulus (on the order of 10 k B T). As a result, a flaccid vesicle(More)
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