Neural network analysis identifies scaffold properties necessary for in vitro chondrogenesis in elastin-like polypeptide biopolymer scaffolds.

The successful design of biomaterial scaffolds for articular cartilage tissue engineering requires an understanding of the impact of combinations of material formulation parameters on diverse and competing functional outcomes of biomaterial performance. This study sought to explore the use of a type of unsupervised artificial network, a self-organizing map, to identify relationships between scaffold formulation parameters (crosslink density, molecular weight, and concentration) and 11 such outcomes (including mechanical properties, matrix accumulation, metabolite usage and production, and histological appearance) for scaffolds formed from crosslinked elastin-like polypeptide (ELP) hydrogels. The artificial neural network recognized patterns in functional outcomes and provided a set of relationships between ELP formulation parameters and measured outcomes. Mapping resulted in the best mean separation amongst neurons for mechanical properties and pointed to crosslink density as the strongest predictor of most outcomes, followed by ELP concentration. The map also grouped formulations together that simultaneously resulted in the highest values for matrix production, greatest changes in metabolite consumption or production, and highest histological scores, indicating that the network was able to recognize patterns amongst diverse measurement outcomes. These results demonstrated the utility of artificial neural network tools for recognizing relationships in systems with competing parameters, toward the goal of optimizing and accelerating the design of biomaterial scaffolds for articular cartilage tissue engineering.

Public goods in networks

This paper considers incentives to provide goods that are non-excludable along social or geographic links. We find, first, that networks can lead to specialization in public good provision. In every social network there is an equilibrium where some individuals contribute and others free ride. In many networks, this extreme is the only outcome. Second, specialization can benefit society as a whole. This outcome arises when contributors are linked, collectively, to many agents. Finally, a new link increases access to public goods, but reduces individual incentives to contribute. Hence, overall welfare can be higher when there are holes in a network. © 2006 Elsevier Inc. All rights reserved.

Analysis of soil carbon transit times and age distributions using network theories

The long-term soil carbon dynamics may be approximated by networks of linear compartments, permitting theoretical analysis of transit time (i.e., the total time spent by a molecule in the system) and age (the time elapsed since the molecule entered the system) distributions. We compute and compare these distributions for different network. configurations, ranging from the simple individual compartment, to series and parallel linear compartments, feedback systems, and models assuming a continuous distribution of decay constants. We also derive the transit time and age distributions of some complex, widely used soil carbon models (the compartmental models CENTURY and Rothamsted, and the continuous-quality Q-Model), and discuss them in the context of long-term carbon sequestration in soils. We show how complex models including feedback loops and slow compartments have distributions with heavier tails than simpler models. Power law tails emerge when using continuous-quality models, indicating long retention times for an important fraction of soil carbon. The responsiveness of the soil system to changes in decay constants due to altered climatic conditions or plant species composition is found to be stronger when all compartments respond equally to the environmental change, and when the slower compartments are more sensitive than the faster ones or lose more carbon through microbial respiration. Copyright 2009 by the American Geophysical Union.