Fujita Critical Curve for a Coupled Diffusion System with Inhomogeneous Neumann Boundary Conditions∗

In this paper, we establish the blow-up theorems of Fujita type for a class of exterior problems of nonlinear diffusion equations subject to inhomogeneous Neumann boundary conditions. The critical Fujita exponents are determined and it is shown that the critical curve belongs to the blow-up case under any nontrivial initial data

A Random Forest Model for Daily PM2.5 Personal Exposure Assessment for a Chinese Cohort

Errors in air pollution exposure assessment are often considered as a major limitation in epidemiological studies. However, it is difficult to obtain accurate personal level exposure on cohort populations due to the often prohibitive expense. Personal exposure estimation models are used in lieu of direct personal exposure measures but still suffer from issues of availability and accuracy. We aim to establish a personal PM2.5 exposure assessment model for a cohort population and assess its performance by applying our model on cohort subjects. We analyzed data from representative sites selected from the subclinical outcomes of polluted air in China (SCOPA-China) cohort study and established a random forest model for estimating daily PM2.5 personal exposure. We also applied the model among subjects recruited in the project mentioned above within the same area and study period to estimate the reliability of the model. The established model showed a good fit with an R2 of 0.81. The model application results showed similar patterns with empirically measured data. Our pilot study provided a validated and feasible modeling approach for assessing daily personal PM2.5 exposure for large cohort populations. The promising model framework can improve PM2.5 exposure assessment accuracy for future environmental health studies of large populations

Approximate controllability of the coupled degenerate system with two boundary controls

Abstract In this paper, we investigate the approximate controllability of the coupled system with boundary degeneracy. The control functions act on the degenerate boundary. We prove the Carleman estimate and the unique continuation of the adjoint system. Then we get the approximate controllability by constructing the control functions

Approximate Controllability of the Degenerate System with the First-Order Term

We consider the approximate controllability of the degenerate system with the first-order term. The first-order term in the equation cannot be controlled by the diffusion term. The system is shown to be approximately controllable by constructing a control by means of its conjugate problem

Critical Curves for A Coupled System of Fast Diffusive Newtonian Filtration Equations

This paper deals with the large time behavior of solutions to the fast diffusive Newtonian filtration equations coupled via the nonlinear boundary sources. The result of Fujita type is obtained by constructing various kinds of upper and lower solutions. Particularly, we show that the critical global existence curve and the critical Fujita curve are the same for the multi-dimensional system, which is quite different from the known results for corresponding one-dimensional problem. 10.1017/S000497271200038

Optimal Control Problems of a Class of Nonlinear Degenerate Parabolic Equations

The optimal control problems of degenerate parabolic equations have many applications in economics, physics, climatology, and so on. Motivated by the applications, we consider the optimal control problems of a class of nonlinear degenerate parabolic equations in this paper. The main result is that we deduce the first order necessary condition for the optimal control problem of nonlinear degenerate parabolic equations by variation method. Moreover, we investigate the uniqueness of the solutions to the optimal control problems. For the linear equations, we obtain the global uniqueness, while for the nonlinear equations, we obtain only the local uniqueness. Finally, we give a numerical example to validate the theoretical results

Carleman estimates and null controllability of a class of singular parabolic equations

In this paper, we consider control systems governed by a class of semilinear parabolic equations, which are singular at the boundary and possess singular convection and reaction terms. The systems are shown to be null controllable by establishing Carleman estimates, observability inequalities and energy estimates for solutions to linearized equations

Screening of reference genes for microRNA analysis in the study of solider caste differentiation of Formosan subterranean termite Coptotermes formosanus Shiraki

Abstract The soldier caste differentiation is a complex process that is governed by the transcriptional regulation and post-transcriptional regulation. microRNAs (miRNAs) are noncoding RNAs that control a wide range of activities. However, their roles in solider caste differentiation are barely studied. RT-qPCR is a powerful tool to study the function of genes. A reference gene is required for normalization for the the relative quantification method. However, no reference gene is available for miRNA quantification in the study of solider caste differentiation of Coptotermes formosanus Shiraki. In this research, in order to screen the suitable reference genes for the study of the roles of miRNAs in solider caste differentiation, the expression levels of 8 candidate miRNA genes were quantified in the head and thorax + abdomen during soldier differentiation. The qPCR data were analyzed using geNorm, NormFinder, BestKeeper, ΔCt method and RefFinder. The normalization effect of the reference genes was evaluated using the let-7-3p. Our study showed that novel-m0649-3p was the most stable reference gene, while U6 was the least stable reference gene. Our study has selected the most stable reference gene, and has paved the way for functional analysis of miRNAs in solider caste differentiation

Methoprene-Induced Genes in Workers of Formosan Subterranean Termites (Coptotermes formosanus Shiraki)

Termites have a distinct polyphenism controlled by concise hormonal and molecular mechanisms. Workers undergo double molts to transform into soldiers (worker–presoldier–soldier). Juvenile hormone analogs, such as methoprene, can induce workers to transform into presoldiers. However, the molecular mechanism underlying the worker-to-presoldier transformation in Coptotermes formosanus Shiraki is still not clear. We sequenced the transcriptome of workers four days after they had fed on methoprene-treated filter paper and control group workers, which fed on acetone-treated filter paper. The transcriptome of C. formosanus was assembled using the de novo assembly method. Expression levels of unigenes in the methoprene-treated group and the control group were compared. The differentially expressed genes were further analyzed by Gene Ontology (GO) term enrichment analysis and Kyoto Encyclopedia of Genes and Genomes pathway enrichment analysis. Tetrapyrrole binding, oxidoreductase activity, and metal ion binding were the only three enriched GO terms. Juvenile hormone synthesis was the first ranked enriched pathway. Carbohydrate, amino acid, and lipid metabolism pathways were also enriched. These three pathways may be related to fat body development, which is critical for presoldier formation. Our results have demonstrated the significance of JH synthesis pathways, and pathways related to fat body development in the artificial induction of presoldiers