In recent work the author has analyzed a number of classical functional search tree and priority queue implementations with the help of the theorem prover Isabelle/HOL. The functional correctness proofs of AVL trees, red-black trees, 2-3 trees, 2-3-4 trees, 1-2 brother trees, AA trees and splay trees could be automated. The amortized logarithmic complexity of skew heaps, splay trees, splay heap...

The randomly diluted elastic network with central force interactions is simulated on the triangular lattice using a constraint analysis of cluster displacement vectors. The exponents for the percolation of splay and total rigidity are found to be the same, ν=1.14±0.1, γ=1.6±0.3, and β=0.46±0.4. The concentration of bonds that are in clusters rigid only with respect to a splay deformation is eva...

This article analyzes modulated phases in liquid crystals, from the long-established cholesteric and blue to recently discovered twist-bend, splay-bend, splay nematic phases, as well twist-grain-boundary (TGB) helical nanofilament variations on smectic phases. The analysis uses concept of four fundamental modes director deformation: twist, bend, splay, a fourth mode related saddle-splay. Each i...

A mystery surrounds the stability properties of the splay-phase periodic solutions to a series array of N Josephson junction oscillators. Contrary to what one would expect from dynamical systems theory, the splay state appears to be neutrally stable for a wide range of system parameters. It has been explained why the splay state must be neutrally stable when the Stewart-McCumber parameter β (a ...

We give a discussion of the Interleave Bound for dynamic optimal binary search, along with some new properties and results. We attempt to apply these results to Splay Trees, in the hope of working towards a proof that splay trees are O(lg lg n)-competitive. Some partial results and conjectures are formulated.

The scaled-particle theory equation of state for the two-dimensional hard-disk fluid on a curved surface is proposed and used to determine the saddle-splay modulus of a particle-laden fluid interface. The resulting contribution to saddle-splay modulus, which is caused by thermal motion of the adsorbed particles, is comparable in magnitude with the saddlesplay modulus of a simple fluid interface.

A bistable liquid crystal display based on the bend and splay configurations has been demonstrated. This display can remain indefinitely either in the splay deformation or in the bend deformation mode. It has the advantages of wide viewing angles, good contrast ratios, faster selection and low operating voltages.

Aspect Oriented Programming (AOP) provides new modularization of software systems through encapsulation of crosscutting functionalities, providing a clear isolation and utilization thereof. The trade-offs are typically a consequence of technical contradictions in requirements. We employ a data structure called a lazy counting based splay tree to analyze the trade-off between the conflicting qua...

We study the organization of topological defects in a system of nematogens confined to the two-dimensional sphere (S2). We first perform Monte Carlo simulations of a fluid system of hard rods (spherocylinders) living in the tangent plane of S2. The sphere is adiabatically compressed until we reach a jammed nematic state with maximum packing density. The nematic state exhibits four +1/2 disclina...