ABSTRACT
In drug discovery, the effectiveness of medicines is based on fitting
the Hill equation (shaped like a sigmoid) to experimental data points.
These data points are sometimes noisy, and often fail to cover the
full range of the sigmoid. This makes curve fitting difficult.
In this talk, we qualitatively and quantitatively "explore" the
geometric properties of this Hill model (slope and curvature) so as to
be able to identify which samples can be fit reliably. In the field of
statistical modeling, this "exploration" is called "domain knowledge",
and this knowledge is then applied to obtain adequate fits on samples
whose fits are uncertain.
This analysis should improve research efforts that aim to use
mathematics and computers to develop better medicines and make the
drug design process less expensive and time consuming. This talk
should appeal to any student interested in mathematics and scientific
inquiry.
