Organic Selection and Social Heredity: The Original Baldwin Effect Revisited

The so-called “Baldwin Effect” has been studied for years in the fields of Artificial Life, Cognitive Science, and Evolutionary Theory across disciplines. This idea is often conflated with genetic assimilation, and has raised controversy in trans-disciplinary scientific discourse due to the many interpretations it has. This paper revisits the “Baldwin Effect” in Baldwin’s original spirit from a joint historical, theoretical and experimental approach. Social Heredity – the inheritance of cultural knowledge via non-genetic means in Baldwin’s term – is also taken into consideration. I shall argue that the Baldwin Effect can occur via social heredity without necessity for genetic assimilation. Computational experiments are carried out to show that when social heredity is permitted with high fidelity, there is no need for the assimilation of acquired characteristics; instead the Baldwin Effect occurs as promoting more plasticity to facilitate future intelligence. The role of mind and intelligence in evolution and its implications in an extended synthesis of evolution are briefly discussed

H\"older regularity of the 2D dual semigeostrophic equations via analysis of linearized Monge-Amp\`ere equations

We obtain the H\"older regularity of time derivative of solutions to the dual semigeostrophic equations in two dimensions when the initial potential density is bounded away from zero and infinity. Our main tool is an interior H\"older estimate in two dimensions for an inhomogeneous linearized Monge-Amp\`ere equation with right hand side being the divergence of a bounded vector field. As a further application of our H\"older estimate, we prove the H\"older regularity of the polar factorization for time-dependent maps in two dimensions with densities bounded away from zero and infinity. Our applications improve previous work by G. Loeper who considered the cases of densities sufficiently close to a positive constant.Comment: v2: title slight changed; some typos fixe

The determinantal ideals of extended Hankel matrices

In this paper, we use the tools of Gr\"{o}bner bases and combinatorial secant varieties to study the determinantal ideals $I_t$ of the extended Hankel matrices. Denote by $c$-chain a sequence $a_1,\...,a_k$ with $a_i+c<a_{i+1}$ for all $i=1,\...,k-1$. Using the results of $c$-chain, we solve the membership problem for the symbolic powers $I_t^{(s)}$ and we compute the primary decomposition of the product $I_{t_1}\... I_{t_k}$ of the determinantal ideals. Passing through the initial ideals and algebras we prove that the product $I_{t_1}\... I_{t_k}$ has a linear resolution and the multi-homogeneous Rees algebra \Rees(I_{t_1},\...,I_{t_k}) is defined by a Gr\"obner basis of quadrics