Interdisciplinary Workshop on Cancer & Hybrid Dynamic Systems
Friday, October 30, 2009
An Overview of SEER Data Analysis
Dr. Sara Sambandham
The Marshall Differential Analyzer: A Physical Interpretation of Mathematics
Dr. Bonita A. Lawrence
Richard Merritt and Devon Tivener
Mechanical integration is an idea dating back to the late 1800's discovered by James Thomson, brother of Lord Kelvin. This idea was then expanded to build a calculating machine, called a differential analyzer, by Vannevar Bush (M.I.T.) in 1929. The Marshall University Differential Analyzer Team has followed in the footsteps of Dr. Bush and a gentleman named Dr. Arthur Porter, who was the first to build a differential analyzer in England when he was a student of Dr. Douglas Hartree. He built his machine of Meccano components, the British version of Erector Set. In the early days of Arthur Porter’s research, the machine was used to solve ordinary differential analyzers of the time. Dr. Porter’s research proved that the Meccano differential analyzer was well suited for many dynamical systems applications.
The Marshall University Differential Analyzer Team has recently constructed the only two publicly accessible differential analyzers in the USF, a mini two integrator machine and a larger four integrator machine built in the spirit of the Porter Meccano Manchester Differential Analyzer. They are continuing in the spirit of Dr. Porter’s work. However, their comparisons will concern digitally computed solutions using numerical methods for approximations.
In this presentation the Team will give an overview of the Marshall Differential Analyzer Project, the mechanics of the machine and the mathematics that can be described by the mechanics. The mini two integrator differential analyzer (known as Lizzie) will accompany the Team for a live demonstration.
Stability and Applications of Hybrid Fractional
Dr. Sara Sambandham
USF Graduate Students
Statistical Analysis and Modeling of Lung Cancer Mortality Time
Statistical Analysis of Event Related Potentials
Event related potentials (ERPs) obtained in an experiment where subjects were presented with word lists containing words observed with different frequencies and having variable emotional valence, either positive or negative. The objectives of the ongoing analysis include evaluation of existing data reduction methods and identification of key temporal and spatial dynamics that come into play across different classes of stimuli. Moreover, a decision rule for the subsequent recall of a word in single trial analysis is going to be discussed.
Nonlinear stochastic model with time varying coefficients
We first introduce the nonlinear stochastic models with time varying coefficients. Then the algorithm to estimate parameters is outlined. Finally, we apply this model for three data sets, and compare results with other models.
Power law process in cancer analysis
The object of the present study is to propose the power law process also known as non homogenous poison process which is identical to the weibull process in analyzing and modeling different types of cancer, especially breast cancer. The key objective is to study the change of the tumor growth as a function of age. The intensity function within the power law process will give us the rate of change of the tumor growth as a function of time. In addition the key parameter within the intensity function can give us the preliminary indication of the behavior of the tumor subject to a given treatment.
Bayesian Reliability Analysis of the Extreme Value Distribution Subject to Several Priors and the Higgins-Tsokos Loss Function
Bayesian analysis of the reliability function for the three parameter Weibull distribution is developed with respect to the usual life testing procedure, with the scale parameter being treated as a random variable. The Bayesian estimates of the reliability functions are compared with respect to those obtained using the Higgins-Tsokos loss function, considering the general uniform, exponential, inverted gamma and Jeffrey’s as prior densities. Bayesian estimates are obtained by numerical integration techniques. In all cases, a Monte Carlo simulation is carried out to make the comparisons. The Higgins-Tsokos loss function used in conjunction with the Jeffrey’s' prior provided the best performance Bayesian estimate of the reliability function, giving a good approximation to the true reliability function. In addition, the Higgins-Tsokos loss function was found to be as robust as the square error loss function, and slightly more efficient.