Preventing False Discovery in Interactive Data Analysis is Hard

We show that, under a standard hardness assumption, there is no computationally efficient algorithm that given $n$ samples from an unknown distribution can give valid answers to $n^{3+o(1)}$ adaptively chosen statistical queries. A statistical query asks for the expectation of a predicate over the underlying distribution, and an answer to a statistical query is valid if it is "close" to the correct expectation over the distribution. Our result stands in stark contrast to the well known fact that exponentially many statistical queries can be answered validly and efficiently if the queries are chosen non-adaptively (no query may depend on the answers to previous queries). Moreover, a recent work by Dwork et al. shows how to accurately answer exponentially many adaptively chosen statistical queries via a computationally inefficient algorithm; and how to answer a quadratic number of adaptive queries via a computationally efficient algorithm. The latter result implies that our result is tight up to a linear factor in $n.$ Conceptually, our result demonstrates that achieving statistical validity alone can be a source of computational intractability in adaptive settings. For example, in the modern large collaborative research environment, data analysts typically choose a particular approach based on previous findings. False discovery occurs if a research finding is supported by the data but not by the underlying distribution. While the study of preventing false discovery in Statistics is decades old, to the best of our knowledge our result is the first to demonstrate a computational barrier. In particular, our result suggests that the perceived difficulty of preventing false discovery in today's collaborative research environment may be inherent

Polypropylene Mesh Implant and A-prf Membrane for Reconstruction of the Traumatic Defects of the Lateral and Back Wall of the Maxillary Sinus

. Background: The aim of this study was to investigate the possible use of Polypropylene mesh implant and A-PRF membrane for covering the defects of the lateral and back wall of the maxillary sinus after its traumatic damages.Materials: non-resorbable Polypropylene mesh implant was used in 10 patients as a barrier membrane for prevention of adipose tissue herniation into maxillary sinus.Method: 3 D CT was used for assessment of bone fragments position and volumetric parameters of the maxillary sinus before and after surgical repair.Result: Postoperative 3-D CT after 2 months demonstrated effective reestablishment of anatomical configuration of sinus and its volume, absence of pathological inflammatory changes of the sinus mucosa.Conclusion: Polypropylene mesh implant provides effective barrier between soft tissues and maxillary sinus, due to its strength characteristic and biocompatibility

Quantum mechanics is about quantum information

I argue that quantum mechanics is fundamentally a theory about the representation and manipulation of information, not a theory about the mechanics of nonclassical waves or particles. The notion of quantum information is to be understood as a new physical primitive -- just as, following Einstein's special theory of relativity, a field is no longer regarded as the physical manifestation of vibrations in a mechanical medium, but recognized as a new physical primitive in its own right.Comment: 17 pages, forthcoming in Foundations of Physics Festschrift issue for James Cushing. Revised version: some paragraphs have been added to the final section clarifying the argument, and various minor clarifying remarks have been added throughout the tex