Cohabitation effect on the slowdown of the Neolithic expansion

We introduce the effect of cohabitation between generations to a previous model on the slowdown of the Neolithic transition in Europe. This effect consists on the fact that human beings do not leave their children alone when they migrate, but on the contrary they cohabit until their children reach adulthood. We also use archaeological data to estimate the variation of the Mesolithic population density with distance, and use this information to predict the slowdown of the Neolithic front speed. The new equation leads to a substantial correction, up to 37%, relative to previous results. The new model is able to provide a satisfactory explanation not only to the relative speed but also to the absolute speed of the Neolithic front obtained from archaeological data

The Role of the Delay Time in the Modeling of Biological Range Expansions

The time interval between successive migrations of biological species causes a delay time in the reaction-diffusion equations describing their space-time dynamics. This lowers the predicted speed of the waves of advance, as compared to classical models. It has been shown that this delay-time effect improves the modeling of human range expansions. Here, we demonstrate that it can also be important for other species. We present two new examples where the predictions of the time-delayed and the classical (Fisher) approaches are compared to experimental data. No free or adjustable parameters are used. We show that the importance of the delay effect depends on the dimensionless product of the initial growth rate and the delay time. We argue that the delay effect should be taken into account in the modeling of range expansions for biological species

Speed of travelling fronts: Two-dimensional and ballistic dispersal probability distributions

The speed of traveling fronts for a two-dimensional model of a delayed reactiondispersal process is derived analytically and from simulations of molecular dynamics. We show that the one-dimensional (1D) and two-dimensional (2D) versions of a given kernel do not yield always the same speed. It is also shown that the speeds of time-delayed fronts may be higher than those predicted by the corresponding non-delayed models. This result is shown for systems with peaked dispersal kernels which lead to ballistic transport

Larock Reaction in the synthesis of heterocyclic compounds

The indole ring is one of the most common features in natural products and small molecules with important bioactivity. Larock reported a new methodology for the synthesis of the indole ring system based on the palladium-catalyzed heteroannulation of 2-iodoaniline and substituted alkyne moieties. This procedure was subsequently extended to the preparation of other nitrogen- and oxygen- containing heterocycles. This is the process of choice for the synthesis of a large number of heterocyclic derivatives, as it provides outstanding regioselectivity and good to excellent yields.

Larock Reaction in the synthesis of heterocyclic compounds

The indole ring is one of the most common features in natural products and small molecules with important bioactivity. Larock reported a new methodology for the synthesis of the indole ring system based on the palladium-catalyzed heteroannulation of 2-iodoaniline and substituted alkyne moieties. This procedure was subsequently extended to the preparation of other nitrogen- and oxygen- containing heterocycles. This is the process of choice for the synthesis of a large number of heterocyclic derivatives, as it provides outstanding regioselectivity and good to excellent yields.