Teaching the Logistic Growth Difference Equation Using Spreadsheets

The logistic growth difference equation is often used in biology to model population growth. The terms that satisfy the difference equation have many remarkable mathematical properties such as exhibiting chaotic behavior. Using spreadsheet modeling tools, the properties of logistic growth can be investigated by students in a user friendly environment. Students will learn about useful computational and modeling tools, while also learning about a new area of mathematics that has fascinated many (e.g. James Gleick’s Chaos: Making a New Science is a national best seller). Moreover, the model has many real world applications in biology. Unfortunately, many mathematics and computer science students do not see the logistic growth model because it does not appear in the standard set of required courses. In this paper we describe a how to implement the logistic growth model, and describe related applications and student exercises

Antibacterial Activity of Polymer Coated Cerium Oxide Nanoparticles

Cerium oxide nanoparticles have found numerous applications in the biomedical industry due to their strong antioxidant properties. In the current study, we report the influence of nine different physical and chemical parameters: pH, aeration and, concentrations of MgSO4, CaCl2, KCl, natural organic matter, fructose, nanoparticles and Escherichia coli, on the antibacterial activity of dextran coated cerium oxide nanoparticles. A least-squares quadratic regression model was developed to understand the collective influence of the tested parameters on the anti-bacterial activity and subsequently a computer-based, interactive visualization tool was developed. The visualization allows us to elucidate the effect of each of the parameters in combination with other parameters, on the antibacterial activity of nanoparticles. The results indicate that the toxicity of CeO2 NPs depend on the physical and chemical environment; and in a majority of the possible combinations of the nine parameters, non-lethal to the bacteria. In fact, the cerium oxide nanoparticles can decrease the anti-bacterial activity exerted by magnesium and potassium salts

Antibacterial Activity of Polymer Coated Cerium Oxide Nanoparticles

Cerium oxide nanoparticles have found numerous applications in the biomedical industry due to their strong antioxidant properties. In the current study, we report the influence of nine different physical and chemical parameters: pH, aeration and, concentrations of MgSO4, CaCl2, KCl, natural organic matter, fructose, nanoparticles and Escherichia coli, on the antibacterial activity of dextran coated cerium oxide nanoparticles. A least-squares quadratic regression model was developed to understand the collective influence of the tested parameters on the anti-bacterial activity and subsequently a computer-based, interactive visualization tool was developed. The visualization allows us to elucidate the effect of each of the parameters in combination with other parameters, on the antibacterial activity of nanoparticles. The results indicate that the toxicity of CeO2 NPs depend on the physical and chemical environment; and in a majority of the possible combinations of the nine parameters, non-lethal to the bacteria. In fact, the cerium oxide nanoparticles can decrease the anti-bacterial activity exerted by magnesium and potassium salts

Dot plot showing the distribution of residuals for the regression model described in <b>Table 2</b>.

<p>Dot plot showing the distribution of residuals for the regression model described in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0047827#pone-0047827-t002" target="_blank"><b>Table 2</b></a>.</p

Screen shot of the visualization application showing the anti-bacterial activity of CeO₂ NPs at a) pH 6 and b) pH 8.

<p>The concentration of cations and NOM is set to 0, NPs and <i>E. coli</i> are at 4.3 ppm and 4.63×10⁵ CFU/mL respectively whereas RPM and fructose are set at 200 RPM and 50 ppm respectively.</p

Antibacterial activity of 4.3 ppm cerium oxide nanoparticle complexed with dextran, dextran alone in comparison to control in sterile distilled water.

<p>Antibacterial activity of 4.3 ppm cerium oxide nanoparticle complexed with dextran, dextran alone in comparison to control in sterile distilled water.</p