Counting is one of the most basic procedures in mathematics and statistics. In statistics literature it is usually done via the proportion estimation method. In this article we manifest a radically different counting procedure first proposed in the late 1990’s based on the techniques of quantum computation. It combines two major tools in quantum computation, quantum Fourier transform and quantu...

Empirical probability models for BATSE GRB location errors are developed via a Bayesian analysis of the separations between BATSE GRB locations and locations obtained with the InterPlanetary Network (IPN). Models are compared and their parameters estimated using 392 GRBs with single IPN annuli and 19 GRBs with intersecting IPN annuli. Most of the analysis is for the 4Br BATSE catalog; earlier c...

In 1957, Francis Crick et al. suggested an ingenious explanation for the process of frame maintenance. The idea was based on the notion of comma-free codes. Although Crick's hypothesis proved to be wrong, in 1996, Arquès and Michel discovered the existence of a weaker version of such codes in eukaryote and prokaryote genomes, namely the so-called circular codes. Since then, circular code theory...

Detecting out-of-distribution (OOD) samples is crucial to the safe deployment of a classifier in real world. However, deep neural networks are known be overconfident for abnormal data. Existing works directly design score function by mining inconsistency from in-distribution (ID) and OOD. In this paper, we further complement with reconstruction error, based on assumption that an autoencoder tra...