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The Positive Solutions Of The Matukuma Equation And The Problem Of Finite Radius And Finite Mass, Jurgen Batt, Yi Li
The Positive Solutions Of The Matukuma Equation And The Problem Of Finite Radius And Finite Mass, Jurgen Batt, Yi Li
Yi Li
This work is an extensive study of the 3 different types of positive solutions of the Matukuma equation 1r2(r2ϕ′)′=−rλ−2(1+r2)λ/2ϕp,p>1,λ>0 : the E-solutions (regular at r = 0), the M-solutions (singular at r = 0) and the F-solutions (whose existence begins away from r = 0). An essential tool is a transformation of the equation into a 2-dimensional asymptotically autonomous system, whose limit sets (by a theorem of H. R. Thieme) are the limit sets of Emden–Fowler systems, and serve as to characterizate the different solutions. The emphasis lies on the study of the M-solutions. …
The Statistical Properties Of The Survivor Interaction Contrast, Joseph W. Houpt, James T. Townsend
The Statistical Properties Of The Survivor Interaction Contrast, Joseph W. Houpt, James T. Townsend
Joseph W. Houpt
The Survivor Interaction Contrast (SIC) is a powerful tool for assessing the architecture and stopping rule of a model of mental processes. Despite its demonstrated utility, the methodology has lacked a method for statistical testing until now. In this paper we briefly describe the SIC then develop some basic statistical properties of the measure. These developments lead to a statistical test for rejecting certain classes of models based on the SIC. We verify these tests using simulated data, then demonstrate their use on data from a simple cognitive task.
Functional Principal Components Analysis And The Capacity Coefficient, D. Burns, Joseph W. Houpt, M. J. Endres, J. T. Townsend
Functional Principal Components Analysis And The Capacity Coefficient, D. Burns, Joseph W. Houpt, M. J. Endres, J. T. Townsend
Joseph W. Houpt
The capacity coefficient is a well established measure of the efficiency of processing combined sources of information. It has been applied to measure cognitive processes ranging from audio-visual integration to face perception. Recently, the capacity coefficient has also been applied in various clinical situations. Typical clinical analysis, such as structural equation modeling, use scalar values or vectors with limited length as input. We explored the use of functional principal component analysis (fPCA) to allow researchers to describe the capacity coefficient, a continuous function of time, with a small set of discrete values. The fPCA approach was compared with two simple …
A New Perspective On Visual Word Processing Efficiency, Joseph W. Houpt, James T. Townsend
A New Perspective On Visual Word Processing Efficiency, Joseph W. Houpt, James T. Townsend
Joseph W. Houpt
As a fundamental part of our daily lives, visual word processing has received much attention in the psychological literature. Despite the well established perceptual advantages of word and pseudoword context using accuracy, a comparable effect using response times has been elusive. Some researchers continue to question whether the advantage due to word context is perceptual. We use the capacity coefficient, a well established, response time based measure of efficiency to provide evidence of word processing as a particularly efficient perceptual process to complement those results from the accuracy domain.
Existence Of Traveling Wave Solutions For A Nonlocal Reaction-Diffusion Model Of Influenza A Drift, Joaquin Riviera, Yi Li
Existence Of Traveling Wave Solutions For A Nonlocal Reaction-Diffusion Model Of Influenza A Drift, Joaquin Riviera, Yi Li
Yi Li
In this paper we discuss the existence of traveling wave solutions for a nonlocal reaction-diffusion model of Influenza A proposed in Lin et. al. (2003). The proof for the existence of the traveling wave takes advantage of the different time scales between the evolution of the disease and the progress of the disease in the population. Under this framework we are able to use the techniques from geometric singular perturbation theory to prove the existence of the traveling wave.