| Igor Sokolov, Department of Mechanical Engineering, Department of Biomedical Engineering, Department of Physics, Tufts University, Medford, MA |
| Title: On some emerging mathematical and statistical needs in nanoscience |
| Abstract: The study of surfaces at the nanoscale (done mostly with atomic force microscopy (AFM) these days) allows imaging not only a sample surface but also mapping its physical and chemical properties. As an example, each set of AFM images/maps can be characterized with up to independent 180 parameters (for example, roughness of the rigidity map, fractal dimension of adhesion, etc.). These parameters are important not only to characterize material but for medical diagnostics. If one considers a combination of these parameters as another parameter, the total number of parameters becomes virtually unlimited. If one adds inevitable noise in each of the images, the problem of classification of the surface parameters and their combinations becomes highly nontrivial.
In this talk I will describe several promising applications in which there is a strong need in the mathematical and statistical tools. A particular emphasis will be given in the early detection of cancerous changes at the single cell level. I will show that the analysis of even one particular parameter might be of big interest, and also can bring the need in new mathematical models. Specifically, the parameter of “multifractality” (deviation of cell geometry from fractal) will be analyzed. I will show how this may have potential implication on understanding of the nature of cancer, and maybe identifying new ways to attack on cancer |