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.

Illustrative Application of the 2^nd-Order Adjoint Sensitivity Analysis Methodology to a Paradigm Linear Evolution/Transmission Model: Reaction-Rate Detector Response

This work continues the illustrative application of the “Second Order Comprehensive Adjoint Sensitivity Analysis Methodology” (2nd-CASAM) to a benchmark mathematical model that can simulate the evolution and/or transmission of particles in a heterogeneous medium. The model response considered in this work is a reaction-rate detector response, which provides the average interactions of particles with the respective detector or, alternatively, the time-average of the concentration of a mixture of substances in a medium. The definition of this model response includes both uncertain boundary points of the benchmark, thereby providing both direct and indirect contributions to the response sensitivities stemming from the boundaries. The exact expressions for the 1st- and 2nd-order response sensitivities to the boundary and model parameters obtained in this work can serve as stringent benchmarks for inter-comparing the performances of all (deterministic and statistical) sensitivity analysis methods.

Illustrative Application of the 2^nd-Order Adjoint Sensitivity Analysis Methodology to a Paradigm Linear Evolution/Transmission Model: Point-Detector Response

This work illustrates the application of the “Second Order Comprehensive Adjoint Sensitivity Analysis Methodology” (2nd-CASAM) to a mathematical model that can simulate the evolution and/or transmission of particles in a heterogeneous medium. The model response is the value of the model’s state function (particle concentration or particle flux) at a point in phase-space, which would simulate a pointwise measurement of the respective state function. This paradigm model admits exact closed-form expressions for all of the 1st- and 2nd-order response sensitivities to the model’s uncertain parameters and domain boundaries. These closed-form expressions can be used to verify the numerical results of production and/or commercial software, e.g., particle transport codes. Furthermore, this paradigm model comprises many uncertain parameters which have relative sensitivities of identical magnitudes. Therefore, this paradigm model could serve as a stringent benchmark for inter-comparing the performances of all deterministic and statistical sensitivity analysis methods, including the 2nd-CASAM.

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.

MMALE—A Methodology for Malware Analysis in Linux Environments

In a computer environment,an operating system is prone to malware,and even the Linux operating system is not an exception.In recent years,malware has evolved,and attackers have become more qualified compared to a few years ago.Furthermore,Linux-based systems have become more attractive to cybercriminals because of the increasing use of the Linux operating system in web servers and Internet of Things(IoT)devices.Windows is the most employed OS,so most of the research efforts have been focused on its malware protection rather than on other operating systems.As a result,hundreds of research articles,documents,and methodologies dedicated to malware analysis have been reported.However,there has not been much literature concerning Linux security and protection from malware.To address all these new challenges,it is necessary to develop a methodology that can standardize the required steps to perform the malware analysis in depth.A systematic analysis process makes the difference between good and ordinary malware analyses.Additionally,a deep malware comprehension can yield a faster and much more efficient malware eradication.In order to address all mentioned challenges,this article proposed a methodology for malware analysis in the Linux operating system,which is a traditionally overlooked field compared to the other operating systems.The proposed methodology is tested by a specific Linux malware,and the obtained test results have high effectiveness in malware detection.

Analysis of Methodology for the Application of Stratified Random Sampling with Optimum Allocation： The Case Study of Forest Bioenergy

In this paper, analysis of methodology was realized for the application of stratified random sampling with optimum allocation in the case of a subject of research which concerns the rural population and presents high differentiations among the three strata in which this population could be classified. The rural population of Evros Prefecture （Greece） with criterion the mean altitude of settlements was classified in three strata, the mountainous, semi-mountainous and fiat population for the estimation of mean consumption of forest fuelwood for covering of heating and cooking needs in households of these three strata. The analysis of this methodology includes： （1） the determination of total size of sample for entire the rural population and its allocation to the various strata; （2） the investigation of effectiveness of stratification with the technique of analysis of variance （One-Way ANOVA）; （3） the conduct of sampling research with the realization of face-to-face interviews in selected households and （4） the control of forms of the questionnaire and the analysis of data by using the statistical package for social sciences, SPSS for Windows. All data for the analysis of this methodology and its practical application were taken by the pilot sampling which was realized in each stratum. Relative paper was not found by the review of literature.

Prediction of Apple Fruit Quality by Soil Nutrient Content and Artificial Neural Network

The effect of soil nutrient content on fruit yield and fruit quality is very important.To explore the effect of soil nutrients on apple quality we investigated 200 fruit samples from 40 orchards in Feng County,Jiangsu Province.Soil mineral elements and fruit quality were measured.The effect of soil nutrient content on fruit quality was analyzed by artificial neural network(ANN)model.The results showed that the prediction accuracy was highest(R2=0.851,0.847,0.885,0.678 and 0.746)in mass per fruit(MPF),hardness(HB),soluble solids concentrations(SSC),titratable acid concentration(TA)and solid-acid ratio(SSC/TA),respectively.The sensitivity analysis of the prediction model showed that soil available P,K,Ca and Mg contents had the greatest impact on the quality of apple fruit.Response surface method(RSM)was performed to determine the optimum range of the available P,K,Ca,and Mg contents in orchards In Feng County,which were 10∼20 mg⋅kg^(−1),170∼200 mg⋅kg^(−1),1000∼1500 mg⋅kg^(−1),and 80∼200 mg⋅kg^(−1),respectively.The research also concluded that improving the content of available P and available Ca in orchard soil was crucial to improve apple fruit quality in Feng County,Jiangsu Province.

Set methods of left-turn waiting zone at signalized intersection

To maximize the number of vehicles passing by the stop-line in a cycle and improve the operation efficiency of intersection in China, the settlement of left-turn lane waiting-zone is becoming prevailing. Based on conflicting-point method, the internal mechanism of left-turn flow after stopping line was analyzed through taking postposition left-turn lane waiting-zone intersection for instance. The relationship between the first left-turn vehicle and the last vehicle of previous phase passing the conflicting point was expounded. According to the time of successive arriving of two vehicle flows at conflicting-point, the reasonable layout for waiting area of left-turn vehicles was researched when the clearance index was less than O. The results suggest that the appropriate layout for waiting area of left-turning vehicles can improve the operation efficiency of intersections.

Methodological Analysis of Clinical Articles on Therapy Evaluation Published in Chinese Journal of Integra

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