Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The purpose of this paper is twofold. First,  provide an optimal [EQUATION] bits lor bound for any two-way protocol for the Vector in Subspace Communication Problem which is of bounded total rank. This result complements Raz's [EQUATION] protocol, which has a simple variant of bounded total rank. Second,  present a plausible mathematical conjecture on a measure concentration phenomenon that implies an [EQUATION] lor bound for a general protocol.  prove the conjecture for the subclass of sets that depend only on [EQUATION] directions.
['Uri Grupel']
I am writing a research paper on a idea Sampling on the sphere by mutually orthogonal subspaces
[{"from": "human", "value": "I am writing a research paper on a idea Sampling on the sphere by mutually orthogonal subspaces"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The purpose of this paper is twofold. First,  provide an optimal [EQUATION] bits lor bound for any two-way protocol for the Vector in Subspace Communication Problem which is of bounded total rank. This result complements Raz's [EQUATION] protocol, which has a simple variant of bounded total rank. Second,  present a plausible mathematical conjecture on a measure concentration phenomenon that implies an [EQUATION] lor bound for a general protocol.  prove the conjecture for the subclass of sets that depend only on [EQUATION] directions."}]