Self-replicating molecules are likely to have played a central role in the origin of life. Most scenarios of Darwinian evolution at the molecular level require self-replicators capable of exponential growth, yet only very few exponential replicators have been reported to date and general design criteria for exponential replication are lacking. Here we show that a peptide-functionalized macrocyc...

In a rooted infinite full binary tree, each vertex is the parent of exactly two children. Since there are exactly 2−1 vertices at level less than or equal to n, the infinite binary tree is said to have exponential growth with growth rate 2. Can we readily determine the growth rates of other self-similar infinite trees? We will see that the answer is yes for a class of trees that can be construc...

We document two widespread biases in how consumers perceive the costs and benefits of borrowing and saving, and explore the implications of these biases for household finance. Payment/interest bias is the systematic tendency to underestimate a loan interest rate given other loan terms. Future value bias is the systematic tendency to underestimate a future value given a present value, time horiz...

In this paper we will study the dynamics of the periodic asymmetric oscillator x′′ + q(t)x+ + q−(t)x− = 0, where q, q− ∈ L(R/2πZ) and x+ = max(x, 0), x− = min(x, 0) for x ∈ R. It will be proved that the exponential growth rate χ(x) := lim t→+∞ 1 t log √ (x(t))2 + (x′(t))2 does exist for each non-zero solution x(t) of the oscillator. The properties of these rates, or the Lyapunov exponents, will...