Sensitivity Analysis

The chapter “Sensitivity Analysis” reviews why sensitivity analysis is a critical component of mathematical modeling, and the different ways of approaching it. A sensitivity analysis is an attempt to identify the parts of the model (i.e. structure, parameter values) that are most important for governing the output. It is an important part of modeling because it is used to quantify the degree of uncertainty in the model prediction and, in many cases, is the main goal of the model (i.e. the model was developed to identify the most important ecological processes). The chapter covers the idea of “local” versus “global” sensitivity analysis via individual parameter perturbation, and how interactive effects of parameters can be revealed via Monte Carlo analysis. Structural versus parameter uncertainty is also explained and explored.

Improving the Selection of Vegetation Index Characteristic Wavelengths by Using the PROSPECT Model for Leaf Water Content Estimation

Equivalent water thickness (EWT) is a major indicator for indirect monitoring of leaf water content in remote sensing. Many vegetation indices (VIs) have been proposed to estimate EWT based on passive or active reflectance spectra. However, the selection of the characteristics wavelengths of VIs is mainly based on statistical analysis for specific vegetation species. In this study, a characteristic wavelength selection algorithm based on the PROSPECT-5 model was proposed to obtain characteristic wavelengths of leaf biochemical parameters (leaf structure parameter (N), chlorophyll a + b content (Cab), carotenoid content (Car), EWT, and dry matter content (LMA)). The effect of combined characteristic wavelengths of EWT and different biochemical parameters on the accuracy of EWT estimation is discussed. Results demonstrate that the characteristic wavelengths of leaf structure parameter N exhibited the greatest influence on EWT estimation. Then, two optimal characteristics wavelengths (1089 and 1398 nm) are selected to build a new ratio VI (nRVI = R1089/R1398) for EWT estimation. Subsequently, the performance of the built nRVI and four optimal published VIs for EWT estimation are discussed by using two simulation datasets and three in situ datasets. Results demonstrated that the built nRVI exhibited better performance (R2 = 0.9284, 0.8938, 0.7766, and RMSE = 0.0013 cm, 0.0022 cm, 0.0030 cm for ANGERS, Leaf Optical Properties Experiment (LOPEX), and JR datasets, respectively.) than that the published VIs for EWT estimation. It is demonstrated that the built nRVI based on the characteristic wavelengths selected using the physical model exhibits desirable universality and stability in EWT estimation.

Boundary rounding effect in the hexagonal and oval two-dimensional optical microcavity

In this paper, the boundary rounding effects of two types of non-circular GaN microcavity system are numerically simulated by the finite element method. When the rounding parameter [Formula: see text] of the hexagonal microcavity decreases, the six corners of the regular hexagon are gradually rounded, the results show that the optical mode gradually changes from the hexagonal whispering-gallery mode (WGM) to the perfect circular WGM, and the quality factor of the modes increases correspondingly. For the oval microcavity, the structure parameter [Formula: see text] increases from 0 to 1 when the oval microcavity gradually changes from a stadium cavity to a circular cavity. The simulation results show that the quality factor increases with [Formula: see text], and the optical mode changes from high-leak mode to WGM. Our results demonstrate the effect of the boundary rounding on the mode pattern and quality factor in hexagonal and oval microcavities.

The Final-over-Final Condition, Stringency, and Typological Structure

The Final-over-Final Condition (FOFC; Biberauer, Holmberg, and Roberts 2014 , et seq.) describes an empirical generalization about possible crosslinguistic word orders. This article presents an Optimality Theory account that derives FOFC using constraints in a stringency relationship. It analyzes the resulting typology through Property Theory ( Alber, DelBusso, and Prince 2016 , Alber and Prince in preparation ). A property analysis explicates the internal structure of the typological space, showing how it explains the condition and how the same structure occurs more generally in stringency systems. The theoretical explanation is compared with that in another theory of typological structure, Parameter Hierarchies ( Roberts 2012 ).