Culture is considered an evolutionary adaptation that enhances human reproductive fitness. A common explanation is that social learning, the learning mechanism underlying cultural transmission, enhances fitness by avoiding the extra costs of individual learning. This explanation was disproved by a mathematical model of individual and social learning, showing that social learners can invade a po...

We evaluate several integrals involving generating functions of continuous q-Hermite polynomials in two diierent ways. The resulting identities give new proofs and generalizations of the Rogers-Ramanujan identities. Two quintic transformations are given, one of which immediately proves the Rogers-Ramanujan identities without the Jacobi triple product identity. Similar techniques lead to new tra...

In this work, we give an identity that leads to establishing the operator . Also, introduce polynomials addition, provide Operator proof for generating function with its extension and Rogers formula The bivariate Rogers-Szegö are deduced. allows obtain inverse linearization , which deduce A solution a q-difference equation is introduced expressed in terms of operators method used recover

Controlling the false discovery rate (FDR) is a powerful approach to multiple testing. In many applications, the tested hypotheses have an inherent hierarchical structure. In this paper, we focus on the fixed sequence structure where the testing order of the hypotheses has been strictly specified in advance. We are motivated to study such a structure, since it is the most basic of hierarchical ...