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Navigating the Turbulent Waters of School Reform Guided by Complexity Theory
The goal of this research study has been to develop, implement, and evaluate a school reform design experiment at a continuation high school with low-income, low-performing underrepresented minority students. The complexity sciences served as a theoretical framework for this design experiment. Treating an innovative college preparatory program as a nested complex adaptive system within a larger complex adaptive system, the school, we used features of complex adaptive systems (equilibrium, emergence, self-organization, and feedback loops) as a framework to design a strategy for school reform. The goal was to create an environment for change by pulling the school far from equilibrium using a strategy we call “purposeful perturbations” to disrupt the stable state of the school in a purposeful way. Over the four years of the study, several tipping points were reached, and we developed agent-based simulation models that capture important dynamic properties of the reform at these points. The study draws upon complexity theory in multiple ways that have supported improved education for low-achieving students
On dynamical bit sequences
Let X^{(k)}(t) = (X_1(t), ..., X_k(t)) denote a k-vector of i.i.d. random
variables, each taking the values 1 or 0 with respective probabilities p and
1-p. As a process indexed by non-negative t, is
constructed--following Benjamini, Haggstrom, Peres, and Steif (2003)--so that
it is strong Markov with invariant measure ((1-p)\delta_0+p\delta_1)^k. We
derive sharp estimates for the probability that ``X_1(t)+...+X_k(t)=k-\ell for
some t in F,'' where F \subset [0,1] is nonrandom and compact. We do this in
two very different settings:
(i) Where \ell is a constant; and
(ii) Where \ell=k/2, k is even, and p=q=1/2. We prove that the probability is
described by the Kolmogorov capacitance of F for case (i) and Howroyd's
1/2-dimensional box-dimension profiles for case (ii). We also present
sample-path consequences, and a connection to capacities that answers a
question of Benjamini et. al. (2003)Comment: 25 pages. This a substantial revision of an earlier paper. The
material has been reorganized, and Theorem 1.3 is ne
Real inequality in Europe since 1500
Introducing a concept of real, as opposed to nominal, inequality of income or wealth suggests some historical reinterpretations, buttressed by a closer look at consumption by the rich. The purchasing powers of different income classes depend on how relative prices move. Relative prices affected real inequality more strongly in earlier centuries than in the twentieth. Between 1500 and about 1800, staple food and fuels became dearer, while luxury goods, especially servants, became cheaper, greatly widening the inequality of lifestyles. Peace, industrialization, and globalization reversed this inegalitarian price effect in the nineteenth century, at least for England
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