The First-Order Comprehensive Sensitivity Analysis Methodology (1st-CASAM) for Scalar-Valued Responses: I. Theory

This work presents the first-order comprehensive adjoint sensitivity analysis methodology (1st-CASAM) for computing efficiently, exactly, and exhaustively, the first-order sensitivities of scalar-valued responses (results of interest) of coupled nonlinear physical systems characterized by imprecisely known model parameters, boundaries and interfaces between the coupled systems. The 1st-CASAM highlights the conclusion that response sensitivities to the imprecisely known domain boundaries and interfaces can arise both from the definition of the system’s response as well as from the equations, interfaces and boundary conditions defining the model and its imprecisely known domain. By enabling, in premiere, the exact computations of sensitivities to interface and boundary parameters and conditions, the 1st-CASAM enables the quantification of the effects of manufacturing tolerances on the responses of physical and engineering systems. Ongoing research will generalize the methodology presented in this work, aiming at computing exactly and efficiently higher-order response sensitivities for coupled systems involving imprecisely known interfaces, parameters, and boundaries.

Second-Order Adjoint Sensitivity Analysis Methodology for Computing Exactly Response Sensitivities to Uncertain Parameters and Boundaries of Linear Systems: Mathematical Framework

This work presents the “Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology (2nd-CASAM)” for the efficient and exact computation of 1st- and 2nd-order response sensitivities to uncertain parameters and domain boundaries of linear systems. The model’s response (i.e., model result of interest) is a generic nonlinear function of the model’s forward and adjoint state functions, and also depends on the imprecisely known boundaries and model parameters. In the practically important particular case when the response is a scalar-valued functional of the forward and adjoint state functions characterizing a model comprising N parameters, the 2nd-CASAM requires a single large-scale computation using the First-Level Adjoint Sensitivity System (1st-LASS) for obtaining all of the first-order response sensitivities, and at most N large-scale computations using the Second-Level Adjoint Sensitivity System (2nd-LASS) for obtaining exactly all of the second-order response sensitivities. In contradistinction, forward other methods would require (N2/2 + 3 N/2) large-scale computations for obtaining all of the first- and second-order sensitivities. This work also shows that constructing and solving the 2nd-LASS requires very little additional effort beyond the construction of the 1st-LASS needed for computing the first-order sensitivities. Solving the equations underlying the 1st-LASS and 2nd-LASS requires the same computational solvers as needed for solving (i.e., “inverting”) either the forward or the adjoint linear operators underlying the initial model. Therefore, the same computer software and “solvers” used for solving the original system of equations can also be used for solving the 1st-LASS and the 2nd-LASS. Since neither the 1st-LASS nor the 2nd-LASS involves any differentials of the operators underlying the original system, the 1st-LASS is designated as a “first-level” (as opposed to a “first-order”) adjoint sensitivity system, while the 2nd-LASS is designated as a “second-level” (rather than a “second-order”) adjoint sensitivity system. Mixed second-order response sensitivities involving boundary parameters may arise from all source terms of the 2nd-LASS that involve the imprecisely known boundary parameters. Notably, the 2nd-LASS encompasses an automatic, inherent, and independent “solution verification” mechanism of the correctness and accuracy of the 2nd-level adjoint functions needed for the efficient and exact computation of the second-order sensitivities.

PRELIMINARY COMPARISON OF SENSITIVITY TOWARD PARVO VIRUS H-1 OF HUMAN HEP ATOM A CELLS AND PARAHEPATOMA TISSUE

Preliminary observations on the result of infection by parvovirus of primary cultured cells of human hepatoma and parahepatoma tissue were reported. Human hepatoma and parahepatoma tissue were obtained by the culture method of tissue fragment plating. It was observed that their respective sensitivity to parvovirus H-1 was different. H-1 had inhibitory effect on epithelial cells of hepatoma tissue but without any significant effect on fibroblasts simultaneously, H-l had no effect on epithelial cells and fibroblasts of parahepatoma tissue. Further investigation of the relationship between parvovirus and hepatoma would be helpful not only in elucidating the mechanism of carcinogenesis and its suppression but also in the search of new approach for the treatment of hepatoma.

Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N): I. Mathematical Framework

This work presents the mathematical framework of the “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N),” which generalizes and extends all of the previous works performed to date on this subject. The 5th-CASAM-N enables the exact and efficient computation of all sensitivities, up to and including fifth-order, of model responses to uncertain model parameters and uncertain boundaries of the system’s domain of definition, thus enabling, inter alia, the quantification of uncertainties stemming from manufacturing tolerances. The 5th-CASAM-N provides a fundamental step towards overcoming the curse of dimensionality in sensitivity and uncertainty analysis.

Third Order Adjoint Sensitivity and Uncertainty Analysis of an OECD/NEA Reactor Physics Benchmark: II. Computed Sensitivities

This work presents the results of the exact computation of (180)3 = 5,832,000 third-order mixed sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) experimental benchmark with respect to the benchmark’s 180 microscopic total cross sections. This computation was made possible by applying the Third-Order Adjoint Sensitivity Analysis Methodology developed by Cacuci. The numerical results obtained in this work revealed that many of the 3rd-order sensitivities are significantly larger than their corresponding 1st- and 2nd-order ones, which is contrary to the widely held belief that higher-order sensitivities are all much smaller and hence less important than the first-order ones, for reactor physics systems. In particular, the largest 3rd-order relative sensitivity is the mixed sensitivity of the PERP leakage response with respect to the lowest energy-group (30) total cross sections of 1H (“isotope 6”) and 239Pu (“isotope 1”). These two isotopes are shown in this work to be the two most important parameters affecting the PERP benchmark’s leakage response. By comparison, the largest 1st-order sensitivity is that of the PERP leakage response with respect to the lowest energy-group total cross section of isotope 1H, having the value , while the largest 2nd-order sensitivity is . The 3rd-order sensitivity analysis presented in this work is the first ever such analysis in the field of reactor physics. The consequences of the results presented in this work on the uncertainty analysis of the PERP benchmark’s leakage response will be presented in a subsequent work.

The First-Order Comprehensive Sensitivity Analysis Methodology (1^st-CASAM) for Scalar-Valued Responses: II. Illustrative Application to a Heat Transport Benchmark Model

This work illustrates the application of the 1st-CASAM to a paradigm heat transport model which admits exact closed-form solutions. The closed-form expressions obtained in this work for the sensitivities of the temperature distributions within the model to the model’s parameters, internal interfaces and external boundaries can be used to benchmark commercial and production software packages for simulating heat transport. The 1st-CASAM highlights the novel finding that response sensitivities to the imprecisely known domain boundaries and interfaces can arise both from the definition of the system’s response as well as from the equations, interfaces and boundary conditions that characterize the model and its imprecisely known domain. By enabling, in premiere, the exact computations of sensitivities to interface and boundary parameters and conditions, the 1st-CASAM enables the quantification of the effects of manufacturing tolerances on the responses of physical and engineering systems.

Sodium Stress in the Halophyte Thellungiella halophila and Transcriptional Changes in a thsos1-RNA Interference Line

The plasma membrane Na＋/H＋-antiporter salt overly sensitive1 （SOS1） from the halophytic Arabidopsis-relative Thellungiella halophila （ThSOS1） shows conserved sequence and domain structure with the orthologous genes from Arabidopsis thaliana and other plants. When expression of ThSOSt was reduced by RNA interference （RNAi）, pronounced characteristics of salt-sensitivity were observed. We were interested in monitoring altered transcriptional responses between Thellungiella wild type and thsost-4, a representative RNAi line with particular emphasis on root responses to salt stress at 350 mmol/L NaCI, a concentration that is only moderately stressful for mature wild type plants. Transcript profiling revealed several functional categories of genes that were differently affected in wild-type and RNAi plants. Down-regulation of SOS1 resulted in different gene expression even in the absence of stress. The pattern of gene induction in the RNAi plant under salt stress was similar to that of glycophytic Arabidopsis rather than that of wild type Thellungiella. The RNAi plants failed to down-regulate functions that are normally reduced in wild type Thellungiella upon stress and did not up-regulate functions that characterize the Thellungiella salt stress response. Metabolite changes observed in wild type Thellungiella after salt stress were less pronounced or absent in RNAi plants. Transcript and metabolite behavior suggested SOS1 functions including but also extending its established function as a sodium transporter. The down-regulation of ThSOS1 converted the halophyte Thellungiella into a salt-sensitive plant.