We study the identification and identifiability problems for heat conduction in a nonhomogeneous rod. The identifiability results are established for two different sets of observations. Given a sequence of distributed type observations, the identifiability is proved for conductivities in a piecewise smooth class of functions. In the case of observations taken at finitely many points the identif...

The ultimate goal of data mining is to extract knowledge from massive data. Knowledge is ideally represented as human-comprehensible patterns from which end-users can gain intuitions and insights. Axis-parallel hyper-rectangles provide interpretable generalizations for multi-dimensional data points with numerical attributes. In this dissertation, we study the fundamental problem of rectangle-ba...