8,056 research outputs found
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 of the extended Hankel
matrices. Denote by -chain a sequence with
for all . Using the results of -chain, we solve the membership
problem for the symbolic powers and we compute the primary
decomposition of the product of the determinantal ideals.
Passing through the initial ideals and algebras we prove that the product
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
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