A Power Calculator for the Classical Twin Design

Power is a ubiquitous, though often overlooked, component of any statistical analyses. Almost every funding agency and institutional review board requires that some sort of power analysis is conducted prior to data collection. While there are several excellent on line power calculators for independent observations, twin studies pose unique challenges that are not incorporated into these algorithms. The goal of the current manuscript is to outline a general method for calculating power in twin studies, and to provide functions to allow researchers to easily conduct power analyses for a range of common twin models. Several scenarios are discussed to demonstrate the importance of various factors that influence the power within the classical twin design and to serve as examples for the provided functions

Relating the variability of tone-burst otoacoustic emission and auditory brainstem response latencies to the underlying cochlear mechanics

Forward and reverse cochlear latency and its relation to the frequency tuning of the auditory filters can be assessed using tone bursts (TBs). Otoacoustic emissions (TBOAEs) estimate the cochlear roundtrip time, while auditory brainstem responses (ABRs) to the same stimuli aim at measuring the auditory filter buildup time. Latency ratios are generally close to two and controversy exists about the relationship of this ratio to cochlear mechanics. We explored why the two methods provide different estimates of filter buildup time, and ratios with large inter-subject variability, using a time-domain model for OAEs and ABRs. We compared latencies for twenty models, in which all parameters but the cochlear irregularities responsible for reflection-source OAEs were identical, and found that TBOAE latencies were much more variable than ABR latencies. Multiple reflection-sources generated within the evoking stimulus bandwidth were found to shape the TBOAE envelope and complicate the interpretation of TBOAE latency and TBOAE/ABR ratios in terms of auditory filter tuning

A metaphor for adiabatic evolution to symmetry

In this paper we study a Hamiltonian system with a spatially asymmetric potential. We are interested in the effects on the dynamics when the potential becomes symmetric slowly in time. We focus on a highly simplified non-trivial model problem (a metaphor) to be able to pursue explicit calculations as far as possible. Using the techniques of averaging and adiabatic invariants, we are able to study all bounded solutions, which reveals significant asymmetric dynamics even when the asymmetric contributions to the potential have become negligibly small.Comment: 27 pages, LaTeX 2e, 8 figures include

The dynamics of a low-order coupled ocean-atmosphere model

A system of five ordinary differential equations is studied which combines the Lorenz-84 model for the atmosphere and a box model for the ocean. The behaviour of this system is studied as a function of the coupling parameters. For most parameter values, the dynamics of the atmosphere model is dominant. For a range of parameter values, competing attractors exist. The Kaplan-Yorke dimension and the correlation dimension of the chaotic attractor are numerically calculated and compared to the values found in the uncoupled Lorenz model. In the transition from periodic behaviour to chaos intermittency is observed. The intermittent behaviour occurs near a Neimark-Sacker bifurcation at which a periodic solution loses its stability. The length of the periodic intervals is governed by the time scale of the ocean component. Thus, in this regime the ocean model has a considerable influence on the dynamics of the coupled system.Comment: 20 pages, 15 figures, uses AmsTex, Amssymb and epsfig package. Submitted to the Journal of Nonlinear Scienc

Another analytic view about quantifying social forces

Montroll had considered a Verhulst evolution approach for introducing a notion he called "social force", to describe a jump in some economic output when a new technology or product outcompetes a previous one. In fact, Montroll's adaptation of Verhulst equation is more like an economic field description than a "social force". The empirical Verhulst logistic function and the Gompertz double exponential law are used here in order to present an alternative view, within a similar mechanistic physics framework. As an example, a "social force" modifying the rate in the number of temples constructed by a religious movement, the Antoinist community, between 1910 and 1940 in Belgium is found and quantified. Practically, two temple inauguration regimes are seen to exist over different time spans, separated by a gap attributed to a specific "constraint", a taxation system, but allowing for a different, smooth, evolution rather than a jump. The impulse force duration is also emphasized as being better taken into account within the Gompertz framework. Moreover, a "social force" can be as here, attributed to a change in the limited need/capacity of some population, coupled to some external field, in either Verhulst or Gompertz equation, rather than resulting from already existing but competing goods as imagined by Montroll.Comment: 4 figures, 29 refs., 15 pages; prepared for Advances in Complex System