Search Results

Empirics of the Urban Structure and Its Evolution

Yannis M. Ioannides

in From Neighborhoods to Nations: The Economics of Social Interactions

This chapter examines the empirics of urban structure and evolution. It first considers Zipf's law for cities and the vibrant exchanges both over theory and empirics pertaining to it. It then ... More

This chapter examines the empirics of urban structure and evolution. It first considers Zipf's law for cities and the vibrant exchanges both over theory and empirics pertaining to it. It then discusses the Duranton model that explains three empirical regularities regarding endogenous city formation: a stationary law for city size distributions that is skewed to the right; churning of industries across cities as cities experience rapid changes in their industrial compositions; and the pattern of urban size transitions. The chapter also explores the empirics of urban transitions by focusing on models of urban evolution that allow for general intradistributional dependence; the hierarchy principle of industrial diversity; the link between geography and spatial clustering; and studies of urban structure based on “quasi-natural experiments.” Finally, it assesses global aspects of city size distribution and its evolution.Less

How Electoral Systems Matter

Rein Taagepera

in Predicting Party Sizes: The Logic of Simple Electoral Systems

An electoral system helps determine the number and size distribution of parties in a country, as well as cabinet duration. Electoral systems are expressed in electoral laws. Their impact depends on ... More

An electoral system helps determine the number and size distribution of parties in a country, as well as cabinet duration. Electoral systems are expressed in electoral laws. Their impact depends on the way politicians and voters make use of these laws. Flawed electoral laws can lead to breakdown of democracy or to staleness.Less

Using Size Distributions to Understand the Role of Body Size in Mammalian Community Assembly

S. K. Morgan Ernest

in Animal Body Size: Linking Pattern and Process across Space, Time, and Taxonomic Group

This chapter examines the evidence demonstrating the role body size plays in mammal communities; discusses the important insights that can be obtained by broadening the mammalian research agenda to ... More

This chapter examines the evidence demonstrating the role body size plays in mammal communities; discusses the important insights that can be obtained by broadening the mammalian research agenda to include the use of individual-level body size distributions; and examines the potential benefits of simultaneously exploring and comparing the relationships between individual and species-level body size distributions using data from nine small mammal communities. The highly conserved nature of species size distributions suggests that this distribution may be a fundamental aspect of how mammals assemble, regardless of habitat type or species composition. In contrast, the sensitivity of the body size energy distribution to shifting species composition suggests that the shape of individual-based distributions may be more context specific.Less

Macroecological Patterns of Body Size in Mammals across Time and Space

S. Kathleen Lyons and Felisa A. Smith

in Animal Body Size: Linking Pattern and Process across Space, Time, and Taxonomic Group

This chapter examines the macroecological patterns of body size in mammals across space and time. It addresses the following questions: How similar are overall body size distributions across ... More

This chapter examines the macroecological patterns of body size in mammals across space and time. It addresses the following questions: How similar are overall body size distributions across individual continents and large islands? How similar are overall body size distributions across time in North America? Are present-day patterns warped? Is the relationship between body size and range size consistent across time and space? Are the shapes of body size distributions at the community level consistent across time and space? The results show gross similarities in macroecological patterns across land masses and throughout evolutionary time. Although there are unique aspects to the patterns on individual continents, the shapes of body size distributions and the moments of the distributions are remarkably similar despite their different evolutionary and geological histories.Less

Size-structured models

Louis W. Botsford, J. Wilson White, and Alan Hastings

in Population Dynamics for Conservation

This chapter begins by revisiting the M’Kendrick/von Foerster model, but using size instead of age as the state variable. It then uses the lessons from that model to describe how individual growth ... More

This chapter begins by revisiting the M’Kendrick/von Foerster model, but using size instead of age as the state variable. It then uses the lessons from that model to describe how individual growth and mortality rates determine both stand distributions (a population of mixed ages) and cohort distributions (all one age). In particular, incorporating variability in growth trajectories is shown to be important in obtaining realistic results—though it is not without pitfalls. Ultimately, the numerical calculations required to model size-structured populations for future projections are more challenging than those needed for age structure, so the chapter closes by discussing some mathematical tools that have been developed to accomplish this. These include the integral projection model, a recent approach that is very useful because, while more complex, it has a lot in common with the age-structured models examined in Chapters 3 and 4.Less

Polydisperse and interacting systems

Dmitri I. Svergun, Michel H. J. Koch, Peter A. Timmins, and Roland P. May

in Small Angle X-Ray and Neutron Scattering from Solutions of Biological Macromolecules

Chapter 5 deals with the systems, which deviate from the ideal monodisperse solutions. The most important cases of such systems are (i) solutions of particles differing in size, shape or conformation ... More

Chapter 5 deals with the systems, which deviate from the ideal monodisperse solutions. The most important cases of such systems are (i) solutions of particles differing in size, shape or conformation (such as equilibrium mixtures of oligomers or solutions of flexible macromolecules), and (ii) solutions, where interparticle interactions cannot be neglected (such as concentrated solutions of (charged) particles). The structural analysis procedures for these systems differ from those for monodisperse systems. Indeed, it would make little sense to try to reconstruct the shape or model the structure of a single particle based on the scattering from a mixture or a strongly interacting system. Relevant questions for the characterisation of such systems relate, for example, to the composition of the mixture or the type of interaction potential. The different data-analysis methods employed for polydisperse and interacting systems are considered.Less

Cities as Six-by-Six-Mile Squares: Zipf's Law?

Thomas J. Holmes and Sanghoon Lee (eds)

in Agglomeration Economics

A question in urban economics that has attracted much attention is the extent to which the size distribution of cities obeys Zipf's law. This chapter considers a new approach to looking at population ... More

A question in urban economics that has attracted much attention is the extent to which the size distribution of cities obeys Zipf's law. This chapter considers a new approach to looking at population distributions that sweeps out any decisions made by bureaucrats or politicians. When comparing populations of geographic units, differences fall along two margins. First, one unit can have a larger population than another because it encompasses a greater land area, holding population density fixed. Second, a unit can have a larger population on a fixed amount of land; that is, higher population density. The chapter analyzes size distribution by cutting the map of the continental United States into a uniform grid of six-by-six-mile squares, and examines the distribution of population across the squares and the extent to which Zipf's law holds for each. A joint analysis of the distribution of population of squares within and across metropolitan areas is a fruitful area for further research.Less

The geometry of fracture networks

Pierre M. Adler, Jean-François Thovert, and Valeri V. Mourzenko

in Fractured Porous Media

This chapter deals with the geometry of random networks. The fractures are generally considered as plane objects such as polygons. The most important question relative to these networks is whether ... More

This chapter deals with the geometry of random networks. The fractures are generally considered as plane objects such as polygons. The most important question relative to these networks is whether they percolate or not. In simple terms, can a Maxwell demon or the like go through the whole medium by walking on the fractures without any jump? The concept of percolation is detailed and applied to fracture networks in conjunction with the excluded volume. The dimensionless density is defined as the number of fractures per excluded volume and is shown to control percolation; this quantity is crucial since it plays a major role in the permeability of fracture networks and of fractured porous media as well. Then, the dimensionless density is estimated from data which can be measured along lines (wells, outcrops,...) or on surfaces (quarries, outcrops,...). This chapter ends with extensions such as fractures with power law size distributions and anisotropic orientations.Less

The Way Forward

Felisa A. Smith and S. Kathleen Lyons

in Animal Body Size: Linking Pattern and Process across Space, Time, and Taxonomic Group

This chapter begins by summarizing the book's main themes. First, we can now begin to appreciate just how much variation there is in body size among most groups of animals. Second, there are ... More

This chapter begins by summarizing the book's main themes. First, we can now begin to appreciate just how much variation there is in body size among most groups of animals. Second, there are remarkably consistent patterns in the body size distributions of some taxa across spatial and temporal gradients that may well reflect how organisms acquire and allocate energy. Third, temperature is important. The discussion then turns to the gaps in this compilation, such as the exclusive focus on animals and the lack of detailed species-level phylogeny for most groups, which hampers the ability to examine the influence of evolutionary history on the body size patterns of animals.Less

Statistical description and structural correlations

Walter Steurer and Julia Dshemuchadse

in Intermetallics: Structures, Properties, and Statistics

In this chapter, a statistical analysis of all structures and structure types of the intermetallic compounds contained in the reduced database “Pearson’s Crystal Data” (PCD) is discussed. The goal is ... More

In this chapter, a statistical analysis of all structures and structure types of the intermetallic compounds contained in the reduced database “Pearson’s Crystal Data” (PCD) is discussed. The goal is to identify, analyze, and discuss structural regularities and relationships for improving one’s understanding of the formation and stability of intermetallics, in order to get a flavor of the big picture. The most important ordering parameters used in this analysis are the Mendeleev numbers. Based on them, the distributions of chemical compositions, stoichiometries, and symmetries of the binary and ternary intermetallic compounds are discussed separately, as well as the occurrence and characteristics of the most common structure types. Also of interest is the distribution of the number of representatives of the structure types, which varies in a wide range.Less

Estimating Mature Plays

P.J. Lee

Jo Anne DeGraffenreid (ed.)

in Statistical Methods for Estimating Petroleum Resources

A key objective in petroleum resource evaluation is to estimate oil and gas pool size (or field size) or oil and gas joint probability distributions for a particular ... More

A key objective in petroleum resource evaluation is to estimate oil and gas pool size (or field size) or oil and gas joint probability distributions for a particular population or play. The pool-size distribution, together with the number-of-pools distribution in a play can then be used to predict quantities such as the total remaining potential, the individual pool sizes, and the sizes of the largest undiscovered pools. These resource estimates provide the fundamental information upon which petroleum economic analyses and the planning of exploration strategies can be based. The estimation of these types of pool-size distributions is a difficult task, however, because of the inherent sampling bias associated with exploration data. In many plays, larger pools tend to be discovered during the earlier phases of exploration. In addition, a combination of attributes, such as reservoir depth and distance to transportation center, often influences the order of discovery. Thus exploration data cannot be considered a random sample from the population. As stated by Drew et al. (1988), the form and specific parameters of the parent field-size distribution cannot be inferred with any confidence from the observed distribution. The biased nature of discovery data resulting from selective exploration decision making must be taken into account when making predictions about undiscovered oil and gas resources in a play. If this problem can be overcome, then the estimation of population mean, variance, and correlation among variables can be achieved. The objective of this chapter is to explain the characterization of the discovery process by statistical formulation. To account for sampling bias, Kaufman et al. (1975) and Barouch and Kaufman (1977) used the successive sampling process of the superpopulation probabilistic model (discovery process model) to estimate the mean and variance of a given play. Here we shall discuss how to use superpopulation probabilistic models to estimate pool-size distribution. The models to be discussed include the lognormal (LDSCV), nonparametric (NDSCV), lognormal/nonparametric–Poisson (BDSCV), and the bivariate lognormal, multivariate (MDSCV) discovery process methods. Their background, applications, and limitations will be illustrated by using play data sets from the Western Canada Sedimentary Basin as well as simulated populations. Less

Crystallization of granitic magmas

Anne Nédélec and Jean-Luc Bouchez

in Granites: Petrology, Structure, Geological Setting, and Metallogeny

Important aspects of magma crystallization are examined in detail, from the formation of the first crystal nuclei and their growth to the fate of the late-magmatic processes, such as residual melts, ... More

Important aspects of magma crystallization are examined in detail, from the formation of the first crystal nuclei and their growth to the fate of the late-magmatic processes, such as residual melts, pegmatites and aplites. Orders of crystallization of minerals are presented with respect to the textural observations under the microscope, and magma compositions. Fractional crystallization is considered and illustrated by considerations about the respective concentrations of compatible and incompatible elements. Finally, Subsolidus mineral transformations due to hydrothermal processes and exsolution are considered. Sections deal with nucleation and crystal growth, including crystal size distributions (CSDs), the order in which minerals crystallize, fractional crystallization and magmatic differentiation, late-magmatic processes, and subsolidus mineral transformations.Less

Robert M. Solow

Roger W. Spencer and David A. Macpherson

in Lives of the Laureates: Twenty-three Nobel Economists

This chapter looks at the work of Robert M. Solow, who was awarded the Nobel Prize in 1987. Solow was born in 1924 and recieved his B.A., M.A., and Ph.D.from Harvard University. He started out ... More

This chapter looks at the work of Robert M. Solow, who was awarded the Nobel Prize in 1987. Solow was born in 1924 and recieved his B.A., M.A., and Ph.D.from Harvard University. He started out serving as assistant and associative professor of statistics. He was then appointed as professor of economics. He progressed to become institute professor and institute professor, emeritus, both at MIT. His doctorate thesis presented a model on the dynamics of the size distribution of incomes as the outcome of a random process of employment in terms of changes in wage levels. He also developed his own version of growth theory encompassing capital-theoretic overtones. Among his titles are Linear Programming and Economic Analysis and Monopolistic Competition and Macroeconomic Theory.Less

Other Assessment Methods—An Overview

P.J. Lee

Jo Anne DeGraffenreid (ed.)

in Statistical Methods for Estimating Petroleum Resources

Resource evaluation procedures have evolved along distinct paths, involving a variety of statistical, geochemical, and geological approaches because of different types ... More

Resource evaluation procedures have evolved along distinct paths, involving a variety of statistical, geochemical, and geological approaches because of different types of data and various assumptions that have driven their development. Many methods have been developed so far, but only those methods that have been published and have significantly influenced subsequent development of evaluation procedures are discussed here. The purpose of this chapter is to present an overview of the principles of these methods and identify the direction of future research in this area. Methods discussed include the following: • Geological approach—volumetric yield by analogy, basin classification • Geochemical approach—petroleum systems, burial and thermal history • Statistical approach (methods that were not discussed in previous chapters are discussed here) • Finite population methods—Arps and Roberts’, Bickel’s, Kaufman’s anchored, and Chen and Sinding–Larsen’s geoanchored • Superpopulation methods—USGS log-geometric, Zipf’s law, creaming, and Long’s • The regression method • The fractal method Specific data and assumptions can be applied to each of these methods. Some of the assumptions can be validated by the data whereas others cannot. These methods have their own merits and disadvantages. The geological approach has been used for the past several decades and is a qualitative method. This section discusses the volumetric yield method and the basin classification method. Volumetric yield using the analogous basin method was the earliest method of petroleum resource evaluation applied to frontier basins. It requires knowledge of the volume of a basin and its characteristics (e.g., tectonic, sedimentation, thermal generation, migration, and accumulation). Based on comparative studies, geologists are able to apply a hydrocarbon yield factor per unit volume (i.e., barrels of oil/cubic unit of sediment) from one known basin to an unknown basin with similar characteristics. Thus, for conceptual basins, this provides some information about the richness of an unknown basin. The advantages are the following: 1. It is suitable for the evaluation of conceptual basins. 2. It is easy to understand. 3. It combines geochemical data and/or experience from mature basins. Less