Sensitivity Conjecture and Log-rank Conjecture for functions with small alternating numbers

The Sensitivity Conjecture and the Log-rank Conjecture are among the most important and challenging problems in concrete complexity. Incidentally, the Sensitivity Conjecture is known to hold for monotone functions, and so is the Log-rank Conjecture for $f(x \wedge y)$ and $f(x\oplus y)$ with monotone functions $f$, where $\wedge$ and $\oplus$ are bit-wise AND and XOR, respectively. In this paper, we extend these results to functions $f$ which alternate values for a relatively small number of times on any monotone path from $0^n$ to $1^n$. These deepen our understandings of the two conjectures, and contribute to the recent line of research on functions with small alternating numbers

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A Tribute to Linda Buettner

On April 26, 2012, the gerontological practice, education, research, and care communities lost one of their foremost members with the passing of Dr. Linda (Lin) Lee Buettner, 56. Lin and her partner, Sue Fitzsimmons, were frequent and valued contributors, editorial board members, and reviewers for both the Journal of Gerontological Nursing and Research in Gerontological Nursing, for many years