Research papers

ON THE VALIDATION OF MODELS

Cort J. Willmott

Traditional methods of evaluating geographic models by statistical comparisons between observed and simulated variates are criticized. In particular, it is suggested that the correlation coefficient (r), its square and tests of their statistical significance are inadequate for such purposes. The root mean squared error (RMSE) and related measures as well as a new index of agreement (d) are alternatively presented as superior indices for making such comparisons. Arguments are made for increasing the number of digital algorithms and data plots being published.

Random-matrix physics: spectrum and strength fluctuations

Thomas A. Brody, J. Flores, J.B. French, Pier A. Mello, Aditya Pandey, S.S.M. Wong

It now appears that the general nature of the deviations from uniformity in the spectrum of a complicated nucleus is essentially the same in all regions of the spectrum and over the entire Periodic Table. This behavior, moreover, is describable in terms of standard Hamiltonian ensembles which could be generated on the basis of simple information-theory concepts, and which give also a good account of fluctuation phenomena of other kinds and, apparently, in other many-body systems besides nuclei. The main departures from simple behavior are ascribable to the moderation of the level repulsion by effects due to symmetries and collectivities, for the description of which more complicated ensembles are called for. One purpose of this review is to give a self-contained account of the theory, using methods---sometimes approximate---which are consonant with the usual theory of stochastic processes. Another purpose is to give a proper foundation for the use of ensemble theory, to make clear the origin of the simplicities in the observable fluctuations, and to derive other general fluctuation results. In comparing theory and experiment, the authors give an analysis of much of the nuclear-energy-level data, as well as an extended discussion of observable effects in nuclear transitions and reactions and in the low-temperature thermodynamics of aggregates of small metallic particles.

Random sample consensus

Martin A. Fischler, Robert C. Bolles

A new paradigm, Random Sample Consensus (RANSAC), for fitting a model to experimental data is introduced. RANSAC is capable of interpreting/smoothing data containing a significant percentage of gross errors, and is thus ideally suited for applications in automated image analysis where interpretation is based on the data provided by error-prone feature detectors. A major portion of this paper describes the application of RANSAC to the Location Determination Problem (LDP): Given an image depicting a set of landmarks with known locations, determine that point in space from which the image was obtained. In response to a RANSAC requirement, new results are derived on the minimum number of landmarks needed to obtain a solution, and algorithms are presented for computing these minimum-landmark solutions in closed form. These results provide the basis for an automatic system that can solve the LDP under difficult viewing

Preliminary reference Earth model

Adam M. Dziewoński, Don L. Anderson

Categorization and Representation of Physics Problems by Experts and Novices*

T. H. Michelene, Paul J. Feltovich, Robert Glaser

The representation of physics problems in relation to the organization of physics knowledge is investigated in experts and novices. Four experiments examine (a) the existence of problem categories as a basis for representation; (b) differences in the categories used by experts and novices; (c) differences in the knowledge associated with the categories; and (d) features in the problems that contribute to problem categorization and representation. Results from sorting tasks and protocols reveal that experts and novices begin their problem representations with specifiably different problem categories, and completion of the representations depends on the knowledge associated with the categories. For, the experts initially abstract physics principles to approach and solve a problem representation, whereas novices base their representation and approaches on the problem's literal features.

Scaling concepts in polymer physics

M. Gordon

Evaluating Structural Equation Models with Unobservable Variables and Measurement Error

Claes Fornell, David F. Larcker

The statistical tests used in the analysis of structural equation models with unobservable variables and measurement error are examined. A drawback of the commonly applied chi square test, in addit...

Evaluating Structural Equation Models with Unobservable Variables and Measurement Error

Claes Fornell, David F. Larcker

The statistical tests used in the analysis of structural equation models with unobservable variables and measurement error are examined. A drawback of the commonly applied chi square test, in addition to the known problems related to sample size and power, is that it may indicate an increasing correspondence between the hypothesized model and the observed data as both the measurement properties and the relationship between constructs decline. Further, and contrary to common assertion, the risk of making a Type II error can be substantial even when the sample size is large. Moreover, the present testing methods are unable to assess a model's explanatory power. To overcome these problems, the authors develop and apply a testing system based on measures of shared variance within the structural model, measurement model, and overall model.

Interaction Models for Water in Relation to Protein Hydration

Herman J. C. Berendsen, J. Postma, W. F. van Gunsteren, J. J. Hérmans

REPRODUCTIVE BIOLOGY OF AUSTRALIAN ACACIAS IN THE SOUTH-WESTERN CAPE PROVINCE, SOUTH AFRICA

Suzanne J. Milton, A. V. Hall

Several Australian members of the genus Acacia L. have attained weed status in the Cape Province, South Africa. It is shown that in the Cape the plants are pollinated but lack effective seed predators. Mature plants drop seeds numbering usually in the range 1 100 to 7 000 m−2yr−1. They have a seed-bank in the soil about two to five times this magnitude, about 95 per cent of which is dormant. It appears that the decline of viability with age may be relatively very slow. These findings are shown to be critical in planning control-methods. (Miss S. J. Milton and Dr A. V. Hall, Bolus Herbarium, University of Cape Town.)

Biology of Octopus vulgaris off the east coast of South Africa

M. J. Smale, P. R. Buchan

A Cognitive Model of the Antecedents and Consequences of Satisfaction Decisions

Richard L. Oliver

A model is proposed which expresses consumer satisfaction as a function of expectation and expectancy disconfirmation. Satisfaction, in turn, is believed to influence attitude change and purchase intention. Results from a two-stage field study support the scheme for consumers and nonconsumers of a flu inoculation.

A Cognitive Model of the Antecedents and Consequences of Satisfaction Decisions

Richard L. Oliver

A model is proposed which expresses consumer satisfaction as a function of expectation and expectancy disconfirmation. Satisfaction, in turn, is believed to influence attitude change and purchase i...

A Closed‐form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils

Martinus Th. van Genuchten

Abstract A new and relatively simple equation for the soil‐water content‐pressure head curve, θ( h ), is described in this paper. The particular form of the equation enables one to derive closed‐form analytical expressions for the relative hydraulic conductivity, K r , when substituted in the predictive conductivity models of N.T. Burdine or Y. Mualem. The resulting expressions for K r ( h ) contain three independent parameters which may be obtained by fitting the proposed soil‐water retention model to experimental data. Results obtained with the closed‐form analytical expressions based on the Mualem theory are compared with observed hydraulic conductivity data for five soils with a wide range of hydraulic properties. The unsaturated hydraulic conductivity is predicted well in four out of five cases. It is found that a reasonable description of the soil‐water retention curve at low water contents is important for an accurated prediction of the unsaturated hydraulic conductivity.

Substituent Constants for Correlation Analysis in Chemistry and Biology.

Gordon L. Flynn

Reproductive biology, length‐weight relationship and relative condition of pond raised <i>Tilapia zilli</i> (Gervais)

S. Dadzie, B.C.C. Wangila

In ‘runted’ populations of Tilapia zilli positive correlations were found between maturation stages and the following: gonadosomatic index, gonad weight, fish weight and fish length. The minimum size at maturity was 9·0 cm in males and 11·0 cm in females. The mean fecundity in the ‘stunted’ females was 2359 eggs and it increased with length ( L ) weight (HO and depth ( D ) of the fish. There was, however, no correlation between fecundity and egg size. The results indicated that growth in this ‘stunted’ T. zilli population was not isometric. The relative condition factor ( Kn ) which approached one indicates good condition.

Expert and Novice Performance in Solving Physics Problems

Jill Larkin, John McDermott, Dorothea P. Simon, Herbert A. Simon

Although a sizable body of knowledge is prerequisite to expert skill, that knowledge must be indexed by large numbers of patterns that, on recognition, guide the expert in a fraction of a second to relevant parts of the knowledge store. The knowledge forms complex schemata that can guide a problem's interpretation and solution and that constitute a large part of what we call physical intuition.

A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species

Graham D. Farquhar, Susanne von Caemmerer, Joseph A. Berry

<i>Scaling Concepts in Polymer Physics</i>

P. G. de Gennes, Thomas A. Witten

Atomic hydrogen stabilized

P. V. E. McClintock

Regression Models for Ordinal Data

Peter McCullagh

Summary A general class of regression models for ordinal data is developed and discussed. These models utilize the ordinal nature of the data by describing various modes of stochastic ordering and this eliminates the need for assigning scores or otherwise assuming cardinality instead of ordinality. Two models in particular, the proportional odds and the proportional hazards models are likely to be most useful in practice because of the simplicity of their interpretation. These linear models are shown to be multivariate extensions of generalized linear models. Extensions to non-linear models are discussed and it is shown that even here the method of iteratively reweighted least squares converges to the maximum likelihood estimate, a property which greatly simplifies the necessary computation. Applications are discussed with the aid of examples.

National Council of Teachers of Mathematics

Organized groups of teachers of mathematics or of individuals preparing to become teachers of mathematics may petition the NCTM Board of Directors to become affiliated with the Council. Affiliated Groups are entitled to send a delegate to the delegate Assembly, which is held each year in conjunction with the NCTM Annual Meeting. The Assembly is a highly respected and influential recommending body of the Council that discusses and votes on resolutions concerning matters pertinent to mathematics education.

A Three-Dimensional Conceptual Model of Corporate Performance

Archie B. Carroll

Offered here is a conceptual model that comprehensively describes essential aspects of corporate social performance. The three aspects of the model address major questions of concern to academics and managers alike: (1) What is included in corporate social responsibility? (2) What are the social issues the organization must address? and (3) What is the organization's philosophy or mode of social responsiveness?

Mathematical model for studying genetic variation in terms of restriction endonucleases.

M Nei, Wen‐Hsiung Li

A mathematical model for the evolutionary change of restriction sites in mitochondrial DNA is developed. Formulas based on this model are presented for estimating the number of nucleotide substitutions between two populations or species. To express the degree of polymorphism in a population at the nucleotide level, a measure called "nucleotide diversity" is proposed.