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Systems Biology is quickly becoming a major focus of applied and
computational mathematics research. While traditionally numerics and
continuous modeling techniques have been used, in recent years it has become
apparent that qualitative modeling, data quantization and data mining
questions play a central role for the field. Monotone Boolean functions are
ubiquitous in these models, and, surprisingly, often both the function and
its dual simultaneously convey practically useful information.
This talk will discuss 4 recent applications of Boolean functions in Systems
Biology: We discuss cut sets in metabolic network analysis, structured
resolution of insatisfiability in cellular signaling networks, and
consecutive-1's in ancestral genome reconstruction. Finally we present an
approach to discover protein associations with groups of individuals in
heterogeneous datasets extending the concept of t-frequent sets to that of
t1-frequent but minimally t2-infrequent sets.
[Parts of this talk are based on various joint projects with Elke
Eisenschmidt, Kathrin Niermann and Robert Weismantel (Uni Magdeburg), Tamon
Stephen and Cedric Chauve (SFU Vancouver) as well as Klaus Truemper (UT
Dallas)]
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