Solving Problems of Practice in Education

The authors identify and discuss the many complexities involved in the translation of scientific information in the social sciences into forms usable for solving problems of practice in education. As a means of appropriately handling these complexities and the issues that arise, they prescribe a series of stages to be followed from the advent of a practitioner's situational problem to the design of a response to it. They assert that unless the process of translation is conducted with the prescribed level of understanding, appreciation, and rigor, the application of knowledge will be inaccurate.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68934/2/10.1177_107554708400600103.pd

Vectorial dissipative solitons in vertical-cavity surface-emitting Lasers with delays

We show that the nonlinear polarization dynamics of a vertical-cavity surface-emitting laser placed into an external cavity leads to the formation of temporal vectorial dissipative solitons. These solitons arise as cycles in the polarization orientation, leaving the total intensity constant. When the cavity round-trip is much longer than their duration, several independent solitons as well as bound states (molecules) may be hosted in the cavity. All these solutions coexist together and with the background solution, i.e. the solution with zero soliton. The theoretical proof of localization is given by the analysis of the Floquet exponents. Finally, we reduce the dynamics to a single delayed equation for the polarization orientation allowing interpreting the vectorial solitons as polarization kinks.Comment: quasi final resubmission version, 12 pages, 9 figure

Patchiness and Demographic Noise in Three Ecological Examples

Understanding the causes and effects of spatial aggregation is one of the most fundamental problems in ecology. Aggregation is an emergent phenomenon arising from the interactions between the individuals of the population, able to sense only -at most- local densities of their cohorts. Thus, taking into account the individual-level interactions and fluctuations is essential to reach a correct description of the population. Classic deterministic equations are suitable to describe some aspects of the population, but leave out features related to the stochasticity inherent to the discreteness of the individuals. Stochastic equations for the population do account for these fluctuation-generated effects by means of demographic noise terms but, owing to their complexity, they can be difficult (or, at times, impossible) to deal with. Even when they can be written in a simple form, they are still difficult to numerically integrate due to the presence of the "square-root" intrinsic noise. In this paper, we discuss a simple way to add the effect of demographic stochasticity to three classic, deterministic ecological examples where aggregation plays an important role. We study the resulting equations using a recently-introduced integration scheme especially devised to integrate numerically stochastic equations with demographic noise. Aimed at scrutinizing the ability of these stochastic examples to show aggregation, we find that the three systems not only show patchy configurations, but also undergo a phase transition belonging to the directed percolation universality class.Comment: 20 pages, 5 figures. To appear in J. Stat. Phy

Spatial Pattern Enhances Ecosystem Functioning in an African Savanna

Termites indirectly enhance plant and animal productivity near their mounds, and the uniform spatial patterning of these mounds enhances the overall productivity of the entire landscape