We introduce generalized hypergeometric Bernoulli numbers for Dirichlet characters. study their properties, including relations, expressions and determinants. At the end in Appendix we derive first few of these numbers.

Just as semantic hashing [Salakhutdinov and Hinton2009] can accelerate information retrieval, binary valued embeddings can significantly reduce latency in the retrieval of graphical data. We introduce a simple but effective model for learning such binary vectors for nodes in a graph. By imagining the embeddings as independent coin flips of varying bias, continuous optimization techniques can be...

In this article we investigate the Bernoulli numbers B̂n associated to the formal group laws whose canonical invariant differentials generate the Lucas sequences {Un} and {Vn}. We give explicit expressions for these numbers and prove analogues of Kummer congruences for them.

Usually, in monitoring a proportion p < /em>, the binary observations are considered independent; however, in many real cases, there is a continuous stream of autocorrelated binary observations in which a two-state Markov chain model is applied with first-order dependence. On the other hand, the Bernoulli CUSUM control chart which is not robust to autocorrelation can be applied two-sided co...