Matthew Witten

How square is the survival curve of a given species

An investigator-independent parameter, the prolate rectangularity index kappa for describing the so-called rectangularity of biological population survival curves, is introduced, developed, and applied to realworld survival datasets. This new rectangularity parameter is constructed using an intrinsic time scaling that places the intrinsic inflection point time at a value of unity so that species populations may be compared independently of their extrinsic life span distributions. The analytical expressions for the prolate rectangularity index of the theoretical Gompertz and Weibull continuous models are obtained, as are numerical values of this index for discrete experimental population survival data sets from two dissimilar species with orders of magnitude difference in extrinsic life span range. The values of the parameter are also compared for populations of a single species having differing dietary regimens, and for human demographic populations at decade intervals in extrinsic chronological time during the current century. It is found that scaling time, using the survival inflection point, appreciably collapses extrinsic survival profile dispersion among similar populations and allows a more meaningful comparison of profiles among dissimilar populations. Using this method of scaling, demographic populations within the United States are seen to have rectangularity parameter values that have been slowly drifting during this century toward values indicating a higher degree of rectangularity. In recent decades, however, the trend appears to be stabilizing with kappa values indicating no approach towards the theoretical maximum rectangularity. This apparent submaximal stabilization of kappa supports a hypothesis of no genetically pre-determined maximum life span in human populations. Or, if such a maximum exists, we are not currently near it.

Gompertz survival model parameters: Estimation and sensitivity

The Gompertzian model of survival is a frequently used two parameter survival dis- tribution. Standard parameter estimation techniques, such as regression and maximum likelihood analysis, require knowledge of the actual lifespans for parameter estimation to be successful. Studies in the evolutionary biology of aging require good estimates of the age-dependent mortality rate coef- ficient (one of the two model parameters). In this paper, we introduce an alternative algorithm for estimating this parameter. And we discuss the sensitivity of the estimates to changes in the other model parameters.

Might stochasticity and sampling variation be a possible explanation for variation in clonal population survival curves

Biogerontological survival analysis attempts to understand, through the use of mathematical and computer models, how biological and environmental processes affect the dynamics of survival. The survival model parameters are assumed to reflect an average or mean response to some intervention. Further, these parameters are usually assumed to be constant over the time course of the experiment and across the elements of the experimental cohort. In this paper, we introduce stochastic (random) features to the survival curve parameters and we observe how this might affect our interpretation of the biology; as reflected in the estimates of the model parameters. In particular, we provide a possible explanation for variation in parameter estimates within sample populations drawn from a population of genetic clones.

Increasing Our Understanding of Biological Models Through Visual and Sonic Representations: a Cortical Case Study

In this study, general aspects of the rendering of data are discussed, with applications to visual and auditory representations of neurobiological data. Scientific sim ulations or real-world models frequently lead to large quantities of complex numerical output. The generat ing model is often realized through a set of static and/ or dynamic descriptors. The rendering of this descrip tor set is formally considered in terms of mappings that result in visual, sonic, and other sensorial simula tions. The visual and sonic maps are described for complex data resulting from a simulation of the mam malian cerebral cortex. A computational model of sig nal flow in a vertically organized slab of neural tissue in cat area 17 has been developed. The complexity of the data requires both visual and sonic rendering. In this study, a number of issues concerned with render ing complex descriptor sets are discussed, but the em phasis is on sonic orchestration, termed BioSymphics.™

Editorial- the Frankenstein Project: Building a Man in the Machine and the Arrival of the Computational Physician

Philosophie Positif, A. Comte stated, &dquo;Every attempt to employ mathematical methods, in the study of chemical questions, must be considered profoundly irrational and contrary to the spirit of chemistry. If mathematical analysis should ever hold a prominent place in chemistry-an aberration which is happily almost impossible-it would occasion a rapid and widespread degeneration of that science.&dquo; The arrival, in the 1960s, of accessible computing hardware and software allowed simulation modeling to become

A New Approach to the Solution of Neurological Models: Application to the Hodgkin-Huxley and the Fitzhugh-Nagumo Equations

The solution of the Hodgkin-Huxley and the Fitzhugh-Nagumo equations are demonstrated as applications of the decomposition method [1–3] which can be used as a new and useful approach obtaining analytical and physically realistic solutions to neurological models and other biological problems without perturbation, linearization, discretization, or massive computation.