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Abstract: Quenching has been an extremely important natural phenomenon observed in many biomedical and multiphysical procedures, such as a rapid cancer cell progression or internal combustion process. The latter has been playing a crucial rule in optimizations of modern solid fuel rocket engine designs. Mathematically, quenching means the blow-up of temporal derivatives of the solution function u while the function itself remains to be bounded throughout the underlying procedure. This paper studies a semi-adaptive numerical method for simulating solutions of a singular partial differential equation that models a significant number of quenching data streams. Numerical convergence will be investigated as well as verifying that features of the solution is preserved in the approximation. Orders of the convergence will also be validated through experimental procedures. Milne's device will be used for data estimate and initial building-up of our deep neural network (DNN) software. Highly accurate data models will be presented to illustrate theoretical predictions. 

Environmental factors such as prenatal stress are hypothesized to contribute to the development of schizophrenia. Lee and colleagues determined rats exposed to prenatal stress exhibited decreased levels of only one protein, DPYSL2, in their prefrontal cortex and hippocampus. DYPSL2, a protein seen to be inactivated in schizophrenic patients, is important for neuronal development. The C. elegans homolog of DPYSL2, UNC-33, is also found to be critical for axonal outgrowth and synapse formation. Herein, we study the effects of environmental stressors such as increasing temperatures and pathogens on the expression of GFP driven by the unc-33 promoter. Results indicate that neuronal GFP expression was lower in C. elegans exposed to these prenatal stressors, making this the first report denoting an environmental regulation of the unc-33 promoter. This study provides insight into unc-33 and the regulation of its expression in relation to temperature and infection.