220 research outputs found
Estimating differential entropy using recursive copula splitting
A method for estimating the Shannon differential entropy of multidimensional
random variables using independent samples is described. The method is based on
decomposing the distribution into a product of the marginal distributions and
the joint dependency, also known as the copula. The entropy of marginals is
estimated using one-dimensional methods. The entropy of the copula, which
always has a compact support, is estimated recursively by splitting the data
along statistically dependent dimensions. Numerical examples demonstrate that
the method is accurate for distributions with compact and non-compact supports,
which is imperative when the support is not known or of mixed type (in
different dimensions). At high dimensions (larger than 20), our method is not
only more accurate, but also significantly more efficient than existing
approaches
Microscopic Study Reveals the Singular Origins of Growth
P.W. Anderson proposed the concept of complexity in order to describe the
emergence and growth of macroscopic collective patterns out of the simple
interactions of many microscopic agents. In the physical sciences this paradigm
was implemented systematically and confirmed repeatedly by successful
confrontation with reality. In the social sciences however, the possibilities
to stage experiments to validate it are limited. During the 90's a series of
dramatic political and economic events have provided the opportunity to do so.
We exploit the resulting empirical evidence to validate a simple agent based
alternative to the classical logistic dynamics. The post-liberalization
empirical data from Poland confirm the theoretical prediction that the dynamics
is dominated by singular rare events which insure the resilience and
adaptability of the system. We have shown that growth is led by few singular
"growth centers" (Figure 1), that initially developed at a tremendous rate
(Figure3), followed by a diffusion process to the rest of the country and
leading to a positive growth rate uniform across the counties. In addition to
the interdisciplinary unifying potential of our generic formal approach, the
present work reveals the strong causal ties between the "softer" social
conditions and their "hard" economic consequences.Comment: 20 pages, 6 figure
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