Predictions from science and engineering models depend on the values of the model's input parameters. As the number of parameters increases, algorithmic parameter studies like optimization or uncertainty quantification require many more model evaluations. One way to combat this curse of dimensionality is to seek an alternative parameterization with fewer variables that produces comparable predictions. The active subspace is a low-dimensional linear subspace defined by important directions in the model's input space; input perturbations along these directions change the model's prediction more, on average, than perturbations orthogonal to the important directions. We describe a method for checking if a model admits an exploitable active subspace, and we apply this method to a single-diode solar cell model with five input parameters. We find that the maximum power of the solar cell has a dominant one-dimensional active subspace, which enables us to perform thorough parameter studies in one dimension instead of five

Somitogenesis is a process common to all vertebrate embryos in which repeated blocks of cells arise from the presomitic mesoderm (PSM) to lay a foundational pattern for trunk and tail development. Somites form in the wake of passing waves of periodic gene expression that originate in the tailbud and sweep posteriorly across the PSM. Previous work has suggested that the waves result from a spatiotemporally graded control protein that affects the oscillation rate of clock-gene expression. With a minimally constructed mathematical model, we study the contribution of two control mechanisms to the initial formation of this gene-expression wave. We test four biologically motivated model scenarios with either one or two clock protein transcription binding sites, and with or without differential decay rates for clock protein monomers and dimers. We examine the sensitivity of wave formation with respect to multiple model parameters and robustness to heterogeneity in cell population. We find that only a model with both multiple binding sites and differential decay rates is able to reproduce experimentally observed waveforms. Our results show that the experimentally observed characteristics of somitogenesis wave initiation constrain the underlying genetic control mechanisms.

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This paper develops the mathematical foundation for a translation of solar cell short-circuit current from one thermal and spectral irradiance operating condition to another without the use of ill-defined and error-prone temperature coefficients typically employed in solar cell metrology. Using the partial derivative of quantum efficiency with respect to temperature, the conventional isothermal expression for spectral mismatch corrections is modified to account for changes of current due to temperature; this modification completely eliminates the need for short-circuitcurrent temperature coefficients. An example calculation is provided to demonstrate use of the new translation.