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We develop a least mean-squares (LMS) diffusion strategy for sensor network applications where it is desired to estimate parameters of physical phenomena that vary over space. In particular, we consider a regression model with space-varying parameters that captures the system dynamics over time and space. We use a set of basis functions such as sinusoids or B-spline functions to replace the space-variant (local) parameters with space-invariant (global) parameters, and then apply diffusion adaptation to estimate the global representation. We illustrate the performance of the algorithm via simulations. [ABSTRACT FROM PUBLISHER]