The inverse problem associated with electrochemical impedance spectroscopy requiring the solution of a Fredholm integral equation of the first kind is considered. If the underlying physical model is not clearly determined, the inverse problem needs to be solved using a regularized linear least squares problem that is obtained from the discretization of the integral equation. For this system, it is shown that the model error can be made negligible by a change of variables and by extending the effective range of quadrature. This change of variables serves as a right preconditioner that significantly improves the condition of the system. Still, to obtain feasible solutions the additional constraint of non-negativity is required. Simulations with artificial, but realistic, data demonstrate that the use of non-negatively constrained least squares with a smoothing norm provides higher quality solutions than those obtained without the non-negative constraint. Using higher-order smoothing norms also reduces the error in the solutions. The L-curve and residual periodogram parameter choice criteria, which are used for parameter choice with regularized linear least squares, are successfully adapted to be used for the non-negatively constrained Tikhonov least squares problem. Although these results have been verified within the context of the analysis of electrochemical impedance spectroscopy, there is no reason to suppose that they would not be relevant within the broader framework of solving Fredholm integral equations for other applications.
The biological sciences encompass topics considered controversial by the American public, such as evolution and climate change. We believe that the development of climate change education in the biology classroom is better informed by an understanding of the history of the teaching of evolution. A common goal for science educators should be to engender a greater respect for and appreciation of science among students while teaching specific content knowledge. Citizen science has emerged as a viable yet underdeveloped method for engaging students of all ages in key scientific issues that impact society through authentic data-driven scientific research. Where successful, citizen science may open avenues of communication and engagement with the scientific process that would otherwise be more difficult to achieve. Citizen science projects demonstrate versatility in education and the ability to test hypotheses by collecting large amounts of often publishable data. We find a great possibility for science education research in the incorporation of citizen science projects in curriculum, especially with respect to “hot topics” of socioscientific debate based on our review of the findings of other authors. Journal of Microbiology & Biology Education.