Epistemology and the Role of Mathematics in Translational Science

Festschrift in Honor of Jaakko Astola on the Occasion of his 60th Birthday, eds. I. Tabus, K. Egiazarian and M. Gabbouj, Tampere International Center for Signal Processing, TICSP Series #47, 60-78, 2009

Abstract

The terminology “translational science” has recently become very popular; however, there has been little effort to give it an epistemological characterization and thereby give it meaning as a scientific enterprise. This paper takes a step in that direction by recognizing that translational science must begin with the epistemology of science and, rooted in the scientific epistemology, extend that epistemology to encompass human actions in the physical world. The road taken here is to consider the classical understanding of operators on random processes in terms of analysis and synthesis, and to delineate their epistemological domains. The main focus of the paper is on synthesis as translational science, in which synthesis is characterized via operator optimization as opposed to being left to trial and error. Three translational settings are used as illustrations, the unity of these theories within the context of translational science being emphasized: (1) the Wiener-Kolmogorov founding paradigm of optimal linear filters in the context of canonical signal representation, (2) the analogous optimal nonlinear filter theory for images in the context of granulometric spectral representation, and (3) the determination of optimal therapeutic strategies based on structural intervention in gene regulatory networks. The paper closes with some comments on the demands imposed by an epistemologically rigorous approach to translational science.