Trading Information Complexity for Error

We consider the standard two-party communication model. The central problem studied in this article is how much can one save in information complexity by allowing a certain error. * For arbitrary functions, we obtain lower bounds and upper bounds indicating a gain that is of order Omega(h(epsilon)) and O(h(sqrt{epsilon})). Here h denotes the binary entropy function. * We analyze the case of the two-bit AND function in detail to show that for this function the gain is Theta(h(epsilon)). This answers a question of Braverman et al. [Braverman, STOC 2013]. * We obtain sharp bounds for the set disjointness function of order n. For the case of the distributional error, we introduce a new protocol that achieves a gain of Theta(sqrt{h(epsilon)}) provided that n is sufficiently large. We apply these results to answer another of question of Braverman et al. regarding the randomized communication complexity of the set disjointness function. * Answering a question of Braverman [Braverman, STOC 2012], we apply our analysis of the set disjointness function to establish a gap between the two different notions of the prior-free information cost. In light of [Braverman, STOC 2012], this implies that amortized randomized communication complexity is not necessarily equal to the amortized distributional communication complexity with respect to the hardest distribution. As a consequence, we show that the epsilon-error randomized communication complexity of the set disjointness function of order n is n[C_{DISJ} - Theta(h(epsilon))] + o(n), where C_{DISJ} ~ 0.4827$ is the constant found by Braverman et al. [Braverman, STOC 2012]

The REST Gene Signature Predicts Drug Sensitivity in Neuroblastoma Cell Lines and Is Significantly Associated with Neuroblastoma Tumor Stage

Neuroblastoma is the most common and deadly solid tumor in children, and there is currently no effective treatment available for neuroblastoma patients. The repressor element-1 silencing transcription (REST) factor has been found to play important roles in the regulation of neural differentiation and tumorigenesis. Recently, a REST signature consisting of downstream targets of REST has been reported to have clinical relevance in both breast cancer and glioblastoma. However it remains unclear how the REST signature works in neuroblastoma. Publicly available datasets were mined and bioinformatic approaches were used to investigate the utility of the REST signature in neuroblastoma with both preclinical and real patient data. The REST signature was found to be associated with drug sensitivity in neuroblastoma cell lines. Further, neuroblastoma patients with enhanced REST activity are significantly associated with higher clinical stages. Loss of heterozygosity on chromosome 11q23, which occurs in a large subset of high-risk neuroblastomas, tends to be correlated with high REST activity, with marginal significance. In conclusion, the REST signature has important implications for targeted therapy, and it is a prognostic factor in neuroblastoma patients