PubMed · 10440840
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P T Becker. 1999. Publishing complexity.. https://doi.org/10.1002/(sici)1098-240x(199908)22%3A4%3C269%3A%3Aaid-nur1%3E3.0.co%3B2-n
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A central problem in science is deciding among competing explanations of data containing random errors. We argue that assessing the "complexity" of explanations is essential to a theoretically well-founded model selection procedure. We formulate model complexity in terms of the geometry of the space of probability distributions. Geometric complexity provides a clear intuitive understanding of several extant notions of model complexity. This approach allows us to reconceptualize the model selection problem as one of counting explanations that lie close to the "truth." We demonstrate the usefulness of the approach by applying it to the recovery of models in psychophysics.
The outcome of the first stage of planetary formation, which is characterized by ballistic agglomeration of preplanetary dust grains due to Brownian motion in the free molecular flow regime of the solar nebula, is still somewhat speculative. We performed a microgravity experiment flown onboard the space shuttle in which we simulated, for the first time, the onset of free preplanetary dust accumulation and revealed the structures and growth rates of the first dust agglomerates in the young solar system. We find that a thermally aggregating swarm of dust particles evolves very rapidly and forms unexpected open-structured agglomerates.
A chaotic attractor containing unstable periodic orbits with different numbers of unstable directions is said to exhibit unstable dimension variability (UDV). We present general mechanisms for the progressive development of UDV in uni- and bidirectionally coupled systems of chaotic elements. Our results are applicable to systems of dissimilar elements without invariant manifolds. We also quantify the severity of UDV to identify coupling ranges where the shadowability and modelability of such systems are significantly compromised.