Treatment Of Heterogeneity Research Articles

Privatization and the distribution of income in the commons

The explicit treatment of heterogeneity among the users of the commons leads to results that differ from those that are now generally accepted in the literature. The owner of the fixed factor is not able to expropriate the rents of privatization. Rather, the resulting distribution of income to the free factor after privatization depends on the technology and the institutional arrangements. This result extends to more than two goods if the decline in the price of the good produced in the commons is sufficient to offset the decline in the marginal product of labor in the rest of the economy.

Finite-Mixture Structural Equation Models for Response-Based Segmentation and Unobserved Heterogeneity

Finite-Mixture Structural Equation Models for Response-Based Segmentation and Unobserved Heterogeneity

SimRoot: Modelling and visualization of root systems

SimRoot, a geometric simulation model of plant root systems, is described. This model employs a data structure titled the Extensible Tree, which is well suited to the type of data required to model root systems. As implemented on Silicon Graphics workstations, the data structure and visualization code provides for continuous viewing of the simulated root system during growth. SimRoot differs from existing models in the explicit treatment of spatial heterogeneity of physiological processes in the root system, and by inclusion of a kinematic treatment of root axes. Examples are provided of the utility of the model in estimating the fractal geometry of simulated root systems in 1, 2, and 3 dimensional space. We envision continued development of the model to incorporate competition from neighboring root systems, linkage with crop simulation models to simulate root-shoot interactions, explicit treatment of soil heterogeneity, and plasticity of root responses to soil factors such as presence of mycorrhizal associations.

Reactive chemical transport within engineered barriers

We consider fully coupled geochemical process systems, and show how they may be cast as differential algebraic systems amenable to numerical solution. Considering reactive transport within engineered barriers, we motivate problems: (1) involving (some) kinetic reactions; (2) in two or more spatial dimensions; (3) incorporating spatial heterogeneity; and (4) with full coupling. The examples considered illustrate the possible treatment of spatial heterogeneity (which causes both channelled flow and stagnant water); the treatment of air-water interfaces as moving-boundaries; corrosion at interfaces; nonlinear feedback when the geochemical and flow problems are full coupled, and the formation of fingering patterns. Our preliminary calculations indicate that such problems are numerically tractable. However, verification and the availability of suitable data remain outstanding issues. Even though these problems are nonlinear, there is range of analytical tools available, and some aspects of the solution can be known quantitatively as well as qualitatively.

A Parameterization for Land–Atmosphere-Cloud Exchange (PLACE): Documentation and Testing of a Detailed Process Model of the Partly Cloudy Boundary Layer over Heterogeneous Land

This paper presents a general description of, and demonstrates the capabilities of, the Parameterization for Land–Atmosphere–Cloud Exchange (PLACE). The PLACE model is a detailed process model of the partly cloudy atmospheric boundary layer and underlying heterogeneous land surfaces. In its development, particular attention has been given to three of the model's subprocesses: the prediction of boundary layer cloud amount, the treatment of surface and soil subgrid heterogeneity, and the liquid water budget. The model includes a three-parameter nonprecipitating cumulus model that feeds back to the surface and boundary layer through radiative effects. Surface heterogeneity in the PLACE model is treated both statistically and by resolving explicit subgrid patches. The model maintains a vertical column of liquid water that is divided into seven reservoirs, from the surface interception store down to bedrock. Five single-day demonstration cases are presented, in which the PLACE model was initialized, run, and compared to field observations from four diverse sites. The model is shown to predict cloud amount well in these while predicting the surface fluxes with similar accuracy. A slight tendency to underpredict boundary layer depth is noted in all cases. Sensitivity tests were also run using anemometer-level forcing provided by the Project for Inter-comparison of Land-surface Parameterization Schemes (PILPS). The purpose is to demonstrate the relative impact of heterogeneity of surface parameters on the predicted annual mean surface fluxes. Significant sensitivity to subgrid variability of certain parameters is demonstrated, particularly to parameters related to soil moisture. A major result is that the PLACE-computed impact of total (homogeneous) deforestation of a rain forest is comparable in magnitude to the effect of imposing heterogeneity of certain surface variables, and is similarly comparable to the overall variance among the other PILPS participant models. Were this result to be bourne out by further analysis, it would suggest that today's average land surface parameterization has little credibility when applied to discriminating the local impacts of any plausible future climate change.

Epidemics: Models and Data

"The problems of understanding and controlling disease raise a range of challenging mathematical and statistical research topics, from broad theoretical issues to specific practical ones. In particular, recent interest in acquired immune deficiency syndrome has stimulated much progress in diverse areas of epidemic modelling, particularly with regard to the treatment of heterogeneity, both between individuals and in mixing of subgroups of the population. At the same time better data and data analysis techniques have become available, and there have been exciting developments in relevant theory.... This progress in specific areas is now being matched by interdisciplinary cooperation aimed at elucidating relationships between the widely varying types of model that have been found useful, to determine their strengths and limitations in relation to basic aims such as understanding, prediction, and evaluation and implementation of control strategies."

A Generalized Index of Diversification: Trends in U.S. Manufacturing

An index of diversification suitable for manufacturing plants and firms is defined as a function of product number, distribution, and dissimilarity. A novel feature of the index is its continuous treatment of product heterogeneity. Using Census of Manufactures data files, the index is constructed for each establishment and each enterprise surveyed in the 1963-1982 censuses. Results are reported at the 2-digit SIC level. While quantifying the upward trend in enterprise diversification, the index reveals an ubiquitous and persistent decline in establishment diversification. Over time, enterprises are shifting toward a more diverse portfolio of increasingly homogeneous plants. Technical economies of scope appear to play little role in explaining the measured increase in enterprise diversification. Copyright 1991 by MIT Press.

Different Epistemologies Beneath Similar Methods: The Case of Causal Loop Thinkers

Causal loop thinkers are found scattered in several fields. Many of the researchers in the following three fields are causal loop thinkers: (1) General Systems Theories; (2) Operations Research and Management Science; (3) System Dynamics. Within each of these three clusters, there are subclusters. Epistemological differences exist among clusters as well as among subclusters. Conceptual cross-fertilization is rare but desirable. Treatment of heterogeneity varies from cluster to cluster and from a subcluster to another, but is absent among most of the causal loop thinkes.

Kinetics of microbial degradation of vascular plant material in two wetland ecosystems.

Vascular plant decomposition was followed during two different years in one freshwater and one marine wetland in southeastern Georgia, USA, using a modified litterbag technique. Chemical analysis of plant material revealed different rates of decomposition for different components of the plant material (soluble components, α-cellulose, hemicellulose, and lignin) and, further, that rates of decomposition of each component changed over time, such that the specific rate of decay for each fraction decreased as decomposition proceeded. Three mathematical models which differen in their treatment of the biochemical heterogeneity of vascular plant detritus were investigated with regard to their relative abilities to describe decomposition kinetics from the field incubations as well as from laboratory microcosm studies with radiolabeled plant material. A decaying coefficient model, which treats plant detritus as a single component but allows for a decreasing specific decomposition rate as material ages, was most successful in describing kinetics of decomposition. This model accomodates the changes in quality of vascular plant detritus resulting from preferential decomposition of more labile components (e.g., non-lignocellulosic material and holocellulose) and the relative accumulation of more refractory components (e.g., lignin) observed with time. The model also accomodates the potential transformation of various plant components into more refractory compounds (humification) during the decomposition process.

The role of mathematical models in helminth population biology

This brief review aims to illustrate how theory can aid in our understanding of the factors that determine the regulation and stability of parasite abundance, and influence the impact of control measures. The current generation of models are obviously crude, and ignore much biological detail, but they are often able to capture qualitative trends observed in real communities. As such, their analysis and investigation can provide important conceptional insights or, in some circumstances, they can be of value in a predictive role (e.g. the impact of chemotherapy in human communities). This field of research, however, is still in its infancy and much remains to be done to improve biological realism in model formulation and to extent the methods of analysis and interpretation. In the latter context, for example, the current analytical methods for the study of the dynamical properties of non-linear systems of differential and partial differential equations are inadequate for many areas of biological application. Future advances in applied mathematics will, therefore, be of great importance. As far as biological realism is concerned, three areas require urgent attention. The first concerns the treatment of heterogeneity in worm loads within host communities. The generative factors of parasite aggregation are many and varied and little is understood at present of how these processes influence a parasite's population response to perturbation induced, for example, by control measures. Stochastic models are required to examine this problem but current work in this area is very limited. The second area concerns immunity to parasitic infection. Few models take account of the substantive body of experimental work which attests to the significance of host responses (both specific and non-specific) to parasite invasion as determinants of parasite abundance within both an individual host and in the community at large. A start has been made in the investigation of models which mimic acquired immunity and immunological “memory” but much refinement and elaboration is needed (Anderson & May, 1985a). In particular, the next generation of models should address the details of antibody-antigen and cell-antigen interactions in individual hosts as well as the broader questions concerning herd immunity. Heterogeneity in immunological responsiveness as a consequence of host nutritional status or genetic background must also be condsidered. The final topic is that of population genetics. Geneticists invariably consider changes in gene frequencies without reference to changes in parasite or host abundance, ecologists and epidemiologists have tended to study changes in abundance without reference to changes in genetic structure while immunologists have focused on the mechanisms of resistance to parasitic infection without reference to population or genetic changes. It is becoming increasingly apparent that host genetic background and genetic heterogeneity within parasite populations (e.g. the malarial parasites of man) are important determinants of observed population events (Medley & Anderson, 1985). Future research must attempt to meld the areas of genetics, population dynamics and immunology. Such an integration presents a fascinating challenge.

Heterogeneity, nonstationarity, and duration-of-stay effects in migration.

"This paper briefly outlines the theoretical problem of the identification of duration-of-stay effects in migration. The empirical studies are critically reviewed with particular emphasis upon their treatment of heterogeneity and nonstationarity. New statistical tests developed by the authors are applied to Wisconsin migration data. These tests suggest that although heterogeneity and nonstationarity are strongly present within the data, duration-of-stay effects appear weak."

Individual Effects in a Nonlinear Model: Explicit Treatment of Heterogeneity in the Empirical Job-Search Model

Individual Effects in a Nonlinear Model: Explicit Treatment of Heterogeneity in the Empirical Job-Search Model

Treatment of Heterogeneity of Variances in Hydrocyanic Acid Data1

AbstractHomogeneity of variance is a basic assumption of the analysis of variance. Hydrocyanic acid potential (HCN‐p) of samples of sorghum (Sorghum bicolor (L.) Moench) plants may vary from nil to the maximum produced by the genotype‐treatment combination, resulting in heterogeneous variances. The purpose of the present study was to further elucidate heterogeneity of variance in HCN‐p data and to employ appropriate treatment of the heterogeneity.‘Greenleaf’ and ‘Piper’ sudangrass (Sorghum sudanese (Piper) Stapf.) and ‘Suhi‐l’, a sorghum ✕ sudangrass hybrid were subjected to five N treatments: (a) no N applied, (b) 67.2 kg/ha at planting, (c) 33.6 kg/ha at planting and 33.6 kg/ha after second harvest, (d) 134.4 kg/ha at planting, and (e) 33.6 kg/ha at planting and 33.6 kg/ha after first, second, and third harvests. When the plants reached a height of 75 cm, they were cut at a height of 20 cm, resulting in four harvests. The cultivar, N, and harvest treatments were analyzed for heterogeneity of variances.For the natural data the treatment means and variances were positively associated and the variances for several treatment comparisons were heterogeneous. Transforming the natural data to common logarithms failed to eliminate the evidence of heterogeneity of variances. Since the data did not meet the assumption of homogeneity of variance, an approximate test of equality of means based upon the assumption of heterogeneity of variance was recommended for the HCN‐p data.Heterogeneity of variances decreases the accuracy of statistical comparisons of means. Since HCN‐p is converted to highly toxic hydrocyanic acid by ruminant animals, accuracy of statistical decisions is critical. Researchers should examine HCN‐p data for evidence of heterogeneity of variances and, if present, employ the approximate test which includes provisions for heterogeneity of variances.

The Resonance Integral of Coated Particles

The effective resonance absorption of coated particles, which are embedded in a graphite matrix, is studied. The effect of a random arrangement of particles on the resonance integral is examined using the radial distribution function derived from the Percus-Yevick equation. A differential equation is proposed to obtain the neutron-beam current from a source particle in a medium in which the distribution function of coated particles is specified. By the use of the neutron beam current and the distribution function as the weight, the fuel-to- fuel collision probability is defined. This collision probability is applied to a RICM-type resonance integral code. The depression of the resonance integral of $sup 238$U due to grain structure amounts to 5 percent in a design study of the multi-purpose high-temperature gas-cooled reactor (HTGCR) at the Japan Atomic Energy Research Institute. The applicabilities of the spherical cell model and of the collision probability in the high-dilution approximation of Lane et al. are tested. These simple procedures give satisfactory results for the treatment of microscopic heterogeneity in the range of the HTGCR design. (auth)