Effective models for charge transport in DNA nanowires

The rapid progress in the field of molecular electronics has led to an increasing interest on DNA oligomers as possible components of electronic circuits at the nanoscale. For this, however, an understanding of charge transfer and transport mechanisms in this molecule is required. Experiments show that a large number of factors may influence the electronic properties of DNA. Though full first principle approaches are the ideal tool for a theoretical characterization of the structural and electronic properties of DNA, the structural complexity of this molecule make these methods of limited use. Consequently, model Hamiltonian approaches, which filter out single factors influencing charge propagation in the double helix are highly valuable. In this chapter, we give a review of different DNA models which are thought to capture the influence of some of these factors. We will specifically focus on static and dynamic disorder.Comment: to appear in "NanoBioTechnology: BioInspired device and materials of the future". Edited by O. Shoseyov and I. Levy. Humana Press (2006

Parametric frailty and shared frailty survival models

Frailty models are the survival data analog to regression models, which account for heterogeneity and random effects. A frailty is a latent multiplicative effect on the hazard function and is assumed to have unit mean and variance theta, which is estimated along with the other model parameters. A frailty model is an heterogeneity model where the frailties are assumed to be individual- or spell-specific. A shared frailty model is a random effects model where the frailties are common (or shared) among groups of individuals or spells and are randomly distributed across groups. Parametric frailty models were made available in Stata with the release of Stata 7, while parametric shared frailty models were made available in a recent series of updates. This article serves as a primer to those fitting parametric frailty models in Stata via the streg command. Frailty models are compared to shared frailty models, and both are shown to be equivalent in certain situations. The user-specified form of the distribution of the frailties (whether gamma or inverse Gaussian) is shown to subtly affect the interpretation of the results. Methods for obtaining predictions that are either conditional or unconditional on the frailty are discussed. An example that analyzes the time to recurrence of infection after catheter insertion in kidney patients is studied. Copyright 2002 by Stata Corporation.parametric survival analysis, frailty, random effects, overdispersion, heterogeneity

Frailty in survival analysis models (parametric frailty, parametric shared frailty, and frailty in Cox models

Frailty models are used to model survival times in the presence of overdispersion or group-specific random effects. The latter are distinguished from the former by the term "shared" frailty models. With the release of Stata 7, estimation of parametric non-shared frailty models is now possible, and the new models appear as extensions to the six parametric survival models previously available. The overdispersion in this case is represented by an unobservable multiplicative effect on the hazard, or frailty. For purposes of estimation this frailty is then assumed to either follow a gamma or inverse-Gaussian distribution. Parametric shared frailty models are the next logical step in the development in this area, and will soon be available as an update to Stata 7. For these models, the random unobservable frailty effects are assumed to follow either a gamma or inverse-Gaussian distribution, but are constrained to be equal over those observations from a given group or panel. Frailty models and shared frailty models for parametric regression with survival data will be discussed, along with avenues for future development at Stata Corp. in this area, in particular, an application of the frailty principle to Cox regression. Series: United Kingdom Stata Users' Group Meeting, 2001

Modeling molecular conduction in DNA wires: Charge transfer theories and dissipative quantum transport

Measurements of electron transfer rates as well as of charge transport characteristics in DNA produced a number of seemingly contradictory results, ranging from insulating behaviour to the suggestion that DNA is an efficient medium for charge transport. Among other factors, environmental effects appear to play a crucial role in determining the effectivity of charge propagation along the double helix. This chapter gives an overview over charge transfer theories and their implication for addressing the interaction of a molecular conductor with a dissipative environment. Further, we focus on possible applications of these approaches for charge transport through DNA-based molecular wires

The role of contacts in molecular electronics

Molecular electronic devices are the upmost destiny of the miniaturization trend of electronic components. Although not yet reproducible on large scale, molecular devices are since recently subject of intense studies both experimentally and theoretically, which agree in pointing out the extreme sensitivity of such devices on the nature and quality of the contacts. This chapter intends to provide a general theoretical framework for modelling electronic transport at the molecular scale by describing the implementation of a hybrid method based on Green function theory and density functional algorithms. In order to show the presence of contact-dependent features in the molecular conductance, we discuss three archetypal molecular devices, which are intended to focus on the importance of the different sub-parts of a molecular two-terminal setup.Comment: 17 pages, 8 figure

An adaptive grid algorithm for one-dimensional nonlinear equations

Richards' equation, which models the flow of liquid through unsaturated porous media, is highly nonlinear and difficult to solve. Step gradients in the field variables require the use of fine grids and small time step sizes. The numerical instabilities caused by the nonlinearities often require the use of iterative methods such as Picard or Newton interation. These difficulties result in large CPU requirements in solving Richards equation. With this in mind, adaptive and multigrid methods are investigated for use with nonlinear equations such as Richards' equation. Attention is focused on one-dimensional transient problems. To investigate the use of multigrid and adaptive grid methods, a series of problems are studied. First, a multigrid program is developed and used to solve an ordinary differential equation, demonstrating the efficiency with which low and high frequency errors are smoothed out. The multigrid algorithm and an adaptive grid algorithm is used to solve one-dimensional transient partial differential equations, such as the diffusive and convective-diffusion equations. The performance of these programs are compared to that of the Gauss-Seidel and tridiagonal methods. The adaptive and multigrid schemes outperformed the Gauss-Seidel algorithm, but were not as fast as the tridiagonal method. The adaptive grid scheme solved the problems slightly faster than the multigrid method. To solve nonlinear problems, Picard iterations are introduced into the adaptive grid and tridiagonal methods. Burgers' equation is used as a test problem for the two algorithms. Both methods obtain solutions of comparable accuracy for similar time increments. For the Burgers' equation, the adaptive grid method finds the solution approximately three times faster than the tridiagonal method. Finally, both schemes are used to solve the water content formulation of the Richards' equation. For this problem, the adaptive grid method obtains a more accurate solution in fewer work units and less computation time than required by the tridiagonal method. The performance of the adaptive grid method tends to degrade as the solution process proceeds in time, but still remains faster than the tridiagonal scheme