Ring lasers are not the only devices that allow rotation sensing with high resolution. This chapter looks at alternative rotation sensing concepts and their physical realization, to put the achievements reported in Chapters 3 and 4 into perspective. We briefly introduce passive Sagnac interferometers, small and large fiber optic gyros, helium SQUID gyros, atom interferometry and Coriolis force-exploiting sensors. It turns out that every application has a different set of requirements, and some types of sensors are better suited for the respective purposes than others. Here we illustrate how the purpose ultimately defines the best technical solution. A book like this would not be complete without looking at solid state ring lasers. However, we also show that in terms of sensitivity and stability, the large ring laser gyroscope takes a prominent role in inertial rotation sensing.

This chapter deals with

• Linear regression notions and mathematical formations

• The assumptions that a linear regression model is based on

• Identifying linear relationships between a dependent variable and independent variables

• Residual plots, leverage and influential points

• Evaluate the degree (effect) to which one variable influences the positive or negative change of another variable

• The geometrical interpretation of the intercept and the slope, and various metrics and tests used to assess the quality of the results

• The interpretation of coefficients

• Studying casual relationships (under specific conditions)

• Building a predictive model by fitting a regression line to the data

• Evaluating the correctness of the model

• Model overfitting

• Ordinary least squares (OLS)

• Exploratory OLS

• Geographically weighted regression (GWR)

After a thorough study of the theory and lab sections, you will be able to

• Distinguish which regression method is more appropriate for the problem at hand and the data available

• Interpret statistics and diagnostics used to evaluate a regression model

• Interpret the outcomes of a regression model such as the coefficient estimates, the scatter plots, the statistics and the maps created

• Identify if relationships, associations or linkages among dependent and independent variables exist

• Analyze data through regression analysis in Matlab

• Conduct exploratory regression analysis in ArcGIS

• Conduct geographically weighted regression in ArcGIS

This chapter deals with

• Spatial autocorrelation and its importance to geographical problems

• Global and local spatial autocorrelation techniques like Moran’s I, Getis-Ord G and Geary C

• Tracing spatial clusters of high values (hot spots) or low values (cold spots)

• Tracing spatial outliers

• Optimized hot spot analysis

• Interpreting the statistical significance of results

• Incremental spatial autocorrelation used to define the appropriate scale of analysis

• The multiple comparison problem and spatial dependence

• Introducing Bonferroni correction and the false discovery rate

• Spatiotemporal autocorrelation analysis using bivariate and differential Local Moran’s I index

• Presenting examples of step-by-step solutions using ArcGIS and GeoDa

After a thorough study of the theory and lab sections, you will be able to

• Distinguish between global and local spatial autocorrelation

• Understand why spatial autocorrelation analysis is relevant to geographical analysis

• Apply local and global indices of spatial autocorrelation like local Moran’s, Getis-Ord Gi and Gi∗

• Use Moran’s I scatter plot to identify patterns

• Identify if clustering of hot or cold spots exist

• Identify and locate spatial outliers

• Use Bivariate and Differential Local Moran’s I to identify if spatiotemporal autocorrelation exists and if changes cluster over time

• Apply these tools using ArcGISand GeoDa

• Interpret the results from both the statistical significance and spatial analysis standpoints

This chapter deals with multivariate statistical methods for data reduction and clustering, commonly used in geographical analysis, including

• Principal component analysis

• Factor analysis

• Multidimensional scaling

• Hierarchical clustering

• -means clustering

• Regionalization (SKATER, REDCAP)

• Density-based clustering (DBSACN, HDBSCAN, OPTICS)

• Similarity analysis (cosine similarity)

After a thorough study of the theory and lab sections, you will be able to

• Understand why multivariate data and statistics are essential in geographical analysis such as in geodemographics

• Understand that observations in multivariate data sets are points in a multidimensional data space

• Understand what principal components are and how they can be mapped in a GIS environment

• Map multidimensional datasets to a 2-D or 3-D representation by multidimensional scaling

• Understand why hierarchical clustering is important to identify the structure of clusters

• Use the k-means algorithm in a geographical problem

• Evaluate the importance of taking into account spatial constraints when clustering (regionalization)

• Use density-based clustering to analyze large datasets of point entities

• Apply similarity analysis to identify common characteristics (profiles) on your spatial entities

• Perform principal component analysis, multidimensional scaling and hierarchical clustering in Matlab

• Conduct k-means clustering, similarity analysis and spatial clustering in ArcGIS

• Conduct k-means clusteringand spatial clustering in GeoDa

This chapter deals with

• Spatial econometrics notions

• Handling spatial dependence and spatial heterogeneity through spatial econometric models

• Diagnostics for spatial dependence (Lagrange multiplier tests)

• Spatial autoregressive model (SAR)

• Spatial error model

• Spatial filtering

• Spatial regression with regimes

• Spatial two-stage least squares (S2SLS)

• Maximum likelihood

• Generalized method of moments (GMM)

After a thorough study of the theory and lab sections, you will be able to

• Distinguish which spatial regression method to use in order to account for spatial dependence and spatial heterogeneity

• Interpret spatial diagnostics used in OLS regression that can guide you to the appropriate spatial regression model

• Build spatial regression models and interpret results

• Identify if spatial dependence or spatial heterogeneity is accounted for by the adopted method

• Conduct spatial econometric analysis through GeoDa space

This chapter deals with

• The notion of exploratory spatial data analysis

• The presentation of descriptive statistics

• Spatial statistics and their importance in analyzing spatial data

• Analyzing univariate data

• Simple exploratory spatial data analysis tools such as histograms, boxplots and other visual methods to get a better insight of spatial datasets

• Bivariate analysis

• Correlation and pairwise correlation

• Normalization, rescaling and adjustments

• An introduction of basic notions of statistical significant tests

• The importance of hypothesis setting in a spatial context

• The importance of normal distribution in classic statistics and how it is integrated into spatial analysis

After a thorough study of the theory and lab sections, you will be able to

• Have a solid knowledge of descriptive statistics

• Use descriptive statistics for univariate analysis

• Understand and use exploratory spatial data analysis techniques to map and analyze variables attached to spatial objects

• Create several plots, link them to maps and identify interesting patterns of data

• Conduct bivariate analysis, identify whether two variables are linearly related and use plots to further examine their relation

• Rescale data to make comparisons between variables easier and also allow for better data handling

• Apply ESDA tools through ArcGIS and GeoDa

This chapter

• Presents the basic concepts, terms and definitions pertaining to spatial analysis

• Introduces a spatial analysis workflow that follows a Describe–Explore–Explain structure

• Presents in detail the reasons why spatial data are special, namely spatial autocorrelation, scale, the modifiable area unit problem, spatial heterogeneity, the edge effects and the ecological fallacy

• Explains why conceptualization of spatial relationships is extremely important in spatial analysis

• Presents the approaches used to conceptualize spatial relationships

• Explains how distance, contiguity/adjacency, neighborhood, proximity polygons and space–time window are used in space conceptualization

• Defines the spatial weights matrix, which is essential to almost every spatial statistic/ technique

• Introduces the real-world project along with the related dataset to be worked throughout the book

After a thorough study of the theory and lab sections, you will be able to

• Implement a comprehensive workflow when you conduct spatial analysis

• Distinguish spatial from nonspatial data

• Understand why spatial data should be treated with new methods (e.g., spatial statistics)

• Understand the importance of applying conceptualization methods according to the problem at hand

• Understand essential terms for conducting spatial analysis as for example distance, contiguity/adjacency, neighborhood, proximity polygons and space–time

• Describe the spatial analysis process to be adopted for solving the real-world project of this book

• Presents the project’s data with ArcGIS and GeoDa

This chapter deals with

• Calculating basic statistics for analyzing geographic distributions including mean center, median center, central feature, standard distance and standard deviational ellipse (centrographics)

• Explaining how these metrics can be used to describe spatial arrangements of different sets of point patterns

• Defining locational and spatial outliers

• Introducing the notions of complete spatial randomness, first-order effects and second-order effects

• Analyzing point patterns through average nearest neighbor analysis

• Ripley’s K function

• Kernel density estimation

• Randomness and the meaning of spatial process in creating point patterns

  After a thorough study of the theory and lab sections, you will be able to

• Use spatial statistics to describe the distribution of point patterns

• Identify locational and spatial outliers

• Use statistical tools and tests to identify if a spatial point pattern is random, clustered or dispersed

• Use Ripley’s K and L functions to define the appropriate scale of analysis

• Use kernel density functions to produce smooth surfaces of points’ intensity over space

• Apply centrographics, conduct point pattern analysis, apply jernel density estimator and trace locational outliers through ArcGIS

This chapter describes the optical properties of leaves at the epidermis and how, to a large extent, the anatomical and morphological structure of the epidermis moderates, controls, and influences the optical properties of the leaf mesophyll and its functioning. We start with the properties of waxes, hairs, and the three-dimensional surface structures and explain many optical phenomena related to scattering of light away from the leaf such as iridescence and specular reflectance, and how surface roughness interacts with water. We discuss how light is focused into the leaf by the epidermal cells, illustrating how this is critical to leaf functions like exchanges of energy and gases.

The purpose of this introductory chapter is to provide a general survey to readers from various backgrounds about how we have thought about leaf properties related to their interactions with light. For example, questions such as “is it colored because of how light contacts with the surface or because some colors of light are absorbed by particular materials?” These questions aroused curiosity about how the nature of interactions with light influence leaf properties, such as observations of leaf color differences on the upper and lower foliar surfaces or why leaves change color in the fall. Investigations from Aristotle up to the 19th century focused on the causes of leaf color and its variation and how these relate to how leaves function. Finally, we introduce some of the earliest studies on the physical mechanisms for the color patterns observed.