Randomization in clinical trials in orthodontics: its significance in research design and methods to achieve it

Randomization is a key step in reducing selection bias during the treatment allocation phase in randomized clinical trials. The process of randomization follows specific steps, which include generation of the randomization list, allocation concealment, and implementation of randomization. The phenomenon in the dental and orthodontic literature of characterizing treatment allocation as random is frequent; however, often the randomization procedures followed are not appropriate. Randomization methods assign, at random, treatment to the trial arms without foreknowledge of allocation by either the participants or the investigators thus reducing selection bias. Randomization entails generation of random allocation, allocation concealment, and the actual methodology of implementing treatment allocation randomly and unpredictably. Most popular randomization methods include some form of restricted and/or stratified randomization. This article introduces the reasons, which make randomization an integral part of solid clinical trial methodology, and presents the main randomization schemes applicable to clinical trials in orthodontics.

Doubly-charged ethane ions: Solution to the dilemma of stability predicted by theory and instability observed in experiment

Potential energy curves have been computed for [C2H6]2+ ions and the results used to interpret the conspicuous absence of these ions in 2E mass spectra and in charge-stripping experiments. The energies and structures of geometry-optimized ground-state singlet and excited-state triplet [C2H6]2+ ions have been determined along with energies for different decomposition barriers and dissociation asymptotes. Although singlet and triplet [C2H6]2+ ions can exist as stable entities, they possess low energy barriers to decomposition. Vertical Franck-Condon transitions, involving electron impact ionization of ethane as well as charge-stripping collisions of [C2H6]+ ions, produce [C2H6]2+ ions which promptly dissociate since they are formed with energies in excess of various decomposition barriers. Appearance energies computed for doubly-charged ethane fragment ions are in accordance with experimental values.

Equivariant inverse spectral theory and toric orbifolds

Let O-2n be a symplectic toric orbifold with a fixed T-n-action and with a tonic Kahler metric g. In [10] we explored whether, when O is a manifold, the equivariant spectrum of the Laplace Delta(g) operator on C-infinity(O) determines O up to symplectomorphism. In the setting of tonic orbifolds we shmilicantly improve upon our previous results and show that a generic tone orbifold is determined by its equivariant spectrum, up to two possibilities. This involves developing the asymptotic expansion of the heat trace on an orbifold in the presence of an isometry. We also show that the equivariant spectrum determines whether the toric Kahler metric has constant scalar curvature. (C) 2012 Elsevier Inc. All rights reserved.