Communication Complexity of Cake Cutting

We study classic cake-cutting problems, but in discrete models rather than using infinite-precision real values, specifically, focusing on their communication complexity. Using general discrete simulations of classical infinite-precision protocols (Robertson-Webb and moving-knife), we roughly partition the various fair-allocation problems into 3 classes: "easy" (constant number of rounds of logarithmic many bits), "medium" (poly-logarithmic total communication), and "hard". Our main technical result concerns two of the "medium" problems (perfect allocation for 2 players and equitable allocation for any number of players) which we prove are not in the "easy" class. Our main open problem is to separate the "hard" from the "medium" classes.Comment: Added efficient communication protocol for the monotone crossing proble

Special Libraries, October 1943

Volume 34, Issue 8https://scholarworks.sjsu.edu/sla_sl_1943/1007/thumbnail.jp

Problems Affecting Labor

Much experimental work has been devoted in comparing the folding behavior of proteins sharing the same fold but different sequence. The recent design of proteins displaying very high sequence identities but different 3D structure allows the unique opportunity to address the protein-folding problem from a complementary perspective. Here we explored by ℙ-value analysis the pathways of folding of three different heteromorphic pairs, displaying increasingly high-sequence identity (namely, 30%, 77%, and 88%), but different structures called G A (a 3-α helix fold) and G B (an α/β fold). The analysis, based on 132 site-directed mutants, is fully consistent with the idea that protein topology is committed very early along the pathway of folding. Furthermore, data reveals that when folding approaches a perfect two-state scenario, as in the case of the G A domains, the structural features of the transition state appear very robust to changes in sequence composition. On the other hand, when folding is more complex and multistate, as for the G Bs, there are alternative nuclei or accessible pathways that can be alternatively stabilized by altering the primary structure. The implications of our results in the light of previous work on the folding of different members belonging to the same protein family are discussed