Abstract: The paper attempts to elucidate the columnar structure
of the cortex by answering the following questions. (1) Why the
cortical neurons with similar interests tend to be vertically arrayed
forming what is known as cortical columns? (2) How to describe the
cortex as a whole in concise mathematical terms? (3) How to design
efficient digital models of the cortex?
Abstract: The paper discusses the mathematics of pattern
indexing and its applications to recognition of visual patterns that are
found in video clips. It is shown that (a) pattern indexes can be
represented by collections of inverted patterns, (b) solutions to
pattern classification problems can be found as intersections and
histograms of inverted patterns and, thus, matching of original
patterns avoided.