Motivated by time-series experimental designs, we develop a model of the act of measurement in the social sciences. Meaningful measurements are represented by operators that obey a non-commutative algebra. Thus, the order in which information is extracted matters. In addition, responses to questions about an attribute depend on whether information about another attribute has previously been ext...

Varying combinations of perceptual cues may be relevant for learning and action-selection. However, storing all possible cue combinations in memory is computationally implausible in sufficiently complex environments due to a state-space explosion. Some psychological models suggest that cue combinations, i.e. chunks, should be generated at a conservative rate (EPAM/CHREST; e.g. Feigenbaum & Simo...

Quality has become one of the core factors for almost all manufacturing and service companies that aim to achieve customer satisfaction. Therefore, improving quality is considered to be one of the efforts that companies consider a must to attain customer loyalty in today’s complex global competitive environment. Studies concluded that any serious endeavour to improve quality will lead to an inc...

The relationship between period doubling bifurcations and Feigenbaum’s constants has been studied for nearly 40 years and this relationship has helped uncover many fundamental aspects of universal scaling across multiple nonlinear dynamical systems. This paper will combine information entropy with symbolic dynamics to demonstrate how period doubling can be defined using these tools alone. In ad...

P. Brunet B. A. Feigenbaum K. Harris C. Laws R. Schwerdtfeger L. Weiss New technology tends to be inaccessible to people with disabilities. Accessibility features are frequently added as the technology matures; doing so late in the cycle incurs significant costs. The initial omission of accessibility features often results from systems designers’ lack of insight into accessibility requirements....

We show that the Feigenbaum-Cvitanović equation can be interpreted as a linearizing equation, and the domain of analyticity of the Feigenbaum fixed point of renormalization as a basin of attraction. There is a natural decomposition of this basin which enables to recover a result of local connectivity by Jiang and Hu for the Feigenbaum Julia set.

A physical measure on the attractor of a system describes the statistical behavior of typical orbits. An example occurs in unimodal dynamics. Namely, all infinitely renormalizable unimodal maps have a physical measure. For Lorenz dynamics, even in the simple case of infinitely renormalizable systems, the existence of physical measures is more delicate. In this article we construct examples of i...

The influence of various convective levels in a melt on a S/L interface is experimentally investigated in a continuous way from pure laminar flows to turbulent ones. Simple description in the Fourier space makes apparent a chaotic and oscillating zones alternance when thermal field is progressively increased. A classical theoretical transition towards the chaos (Feigenbaum mechanism) seems to b...

In 1980, the journal Science published an article of Feigenbaum M. J. Universal Behavior in Nonlinear Systems [1]. This article was a simple mathematical observation concerning one-dimensional maps. Of particular interest in this situation was the fact that the observation was made by simply using a calculator! And over time this work has become a progenitor of serious mathematical sciences. No...

We construct a Markov partition for a Feigenbaum-like mapping. We prove that this Markov partition has bounded nearby geometry property similar to that for a geometrically finite one-dimensional mappings [8]. Using this property, we give a simple proof that any two Feigenbaum-like mappings are topologically conjugate and the conjugacy is quasisymmetric.