As Dobzhansky wrote, nothing in biology makes sense outside the context of the evolutionary theory, and this truth has not been sufficiently explored yet by medicine. We comment on Shanks and Pyles' recently published paper, Evolution and medicine: the long reach of "Dr. Darwin", and discuss some recent advancements in the application of evolutionary theory to carcinogenesis. However, we disagr...

The idea that there are multiple learning systems has become increasingly influential in recent years, with many studies providing evidence that there is both a quick, similarity-based or feature-based system and a more effortful rule-based system. A smaller number of imaging studies have also examined whether neurally dissociable learning systems are detectable. We further investigate this by ...

Shanks (1991) reported experiments that show selective-learning effects in a categorization task, and presented simulations of his data using a connectionist network model implementing the Rescorla-Wagner (R-W) theory of animal conditioning. He concluded that his results (a) support the application of the R-W theory to account for human categorization, and (b) contradict a particular variant of...

We present a new cube root algorithm in finite field Fq with q a power of prime, which extends Cipolla-Lehmer type algorithms and has lower complexity than Tonelli-Shanks type algorithms. Efficient computation of r-th root in Fq has many applications in computational number theory and many other related areas. There are two standard algorithms for computing rth root in finite field. One is Adle...

We discuss a space of Young measures in connection with some variational problems. We use it to present a proof of the Theorem of Tonelli on the existence of minimizing curves. We generalize a recent result of Ambrosio, Gigli and Savaré on the decomposition of the weak solutions of the transport equation. We also prove, in the context of Mather theory, the equality between Closed measures and H...

Given a Tonelli Hamiltonian of class C on the cotangent bundle of a compact surface, we show that there is an open dense set of potentials in the C topology for which the Aubry set is hyperbolic in its energy level.