The genomic era has brought about profound changes in the study of genetic mechanisms, with the infusion of mathematical tools to aid both traditional and novel biological techniques. The underlying biological mechanisms of gene expression, and specifically the logical gene interactions which determine the sequential patterns of transcription, are expected to be very complicated. Such complex systems can essentially be studied in the context of mathematics. Thus it becomes necessary to find appropriate mathematical models for encoding what is already known, not merely for book-keeping purposes, but with the ultimate goal of inferring new information from the logic of the underlying mathematics.
I will introduce a new, topological technique for encoding gene interactions at the transcription level. Our method can in essence be viewed as a high dimensional version of a network. While it is not likely that any mathematical model will succeed in avoiding the problem of high complexity, our topological model addresses the complexity issue by separating the problem into several strata. As well, topological methods make our model amenable to addressing some of the local--global problems, and viewing the functioning genome as a single interactive system.
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