Maximum Getis–Ord Statistic Adjusted for Spatially Autocorrelated Data

Local statistics test the null hypothesis of no spatial association or clustering around the vicinity of a location. To carry out statistical tests, it is assumed that the observations are independent and that they exhibit no global spatial autocorrelation. In this article, approaches to account for global spatial autocorrelation are described and illustrated for the case of the Getis–Ord statistic with binary weights. Although the majority of current applications of local statistics assume that the spatial scale of the local spatial association (as specified via weights) is known, it is more often the case that it is unknown. The approaches described here cover the cases of testing local statistics for the cases of both known and unknown weights, and they are based upon methods that have been used with aspatial data, where the objective is to find changepoints in temporal data. After a review of the Getis–Ord statistic, the article provides a review of its extension to the case where the objective is to choose the best set of binary weights to estimate the spatial scale of the local association and assess statistical significance. Modified approaches that account for spatially autocorrelated data are then introduced and discussed. Finally, the method is illustrated using data on leukemia in central New York, and some concluding comments are made.     

Two-dimensional fiscal competition

This paper analyses commodity tax competition between two neighboringcountries whose governments are tax-revenue maximizers in atwo-dimensional market. The results suggest three conclusionsin a geographical sense. First, a small country sets a lowertax than does a big country, and per capita revenue of the smallcountry is larger than that of the big country. Second, thesetwo countries are subject to severer competitive pressure inthe case of a more curved national border. Finally, the impactof border curvature on tax and revenue differences are alwaysopposite in sign with the impact on tax and revenue ratios.     

The Conceptual Locus of a Two-dimensional Language: Some Implications for Human Responses to Two-dimensional Displays

It is proposed that two-dimensional displays, such as maps, aerial photographs, polygons, etc., may be generated and/or described by two-dimensional languages. A simple perceptual device is posited which utilizes such a language. The device is comprised of at least two components which represent short-term and long-term memory. It is clear that its conceputal locus is in multisystem memory models. Three such models are characterized which provide the necessary and sufficient conditions for the perceptual model posited. Given this conceptual frame, three illustrative sets of implications and experiments for human responses to two-dimensional displays are suggested.     

Analysis of Qualitative Similarity between Surfaces

This paper develops a method for analyzing surfaces with a focus on their qualitative similarity. The method describes the qualitative similarity between surfaces defined in the same region in both quantitative and qualitative ways. Given a location and a direction in the region, mathematical functions evaluate the similarity between surfaces. Integrals of the functions with respect to location and direction give quantitative measures of the total similarity between surfaces. A qualitative method uses spatial characteristics shared by surfaces: α‐peak regions, α‐pit regions, and ß‐monotonic lines. α‐peak and α‐pit regions indicate approximate locations where many surfaces have peaks and pits, respectively. ß‐monotonic lines are line segments on which most surfaces change monotonically in the same direction. Those spatial objects reveal the spatial structure shared by surfaces. The method is applied to the analysis of the daily market structure of a supermarket in Japan as an empirical study.     

Simulating global patterns of Pleistocene hominin morphology

The first ever simulations of global patterns of early Homo morphology are presented here. These simulations are a good match to the known patterns in the fossil record. An enhanced version of the Stepping Out model is presented which simulated global patterns of hominin morphology including genetic drift and the homogenising effects of inter-group exchange. Stepping Out is then used to examine the importance of environmental factors on hominin morphology. The most significant feature of the simulations is an emergent division between the African and Asian populations. The effect of biogeographical factors on this division and other patterning is considered. Throughout, modelling results are interpreted in the context of fossil and archaeological records in order to enhance our understanding of population histories of hominin groups.     

Two-dimensional high-resolution imaging of the equatorial plasma fountain

The first visual representation of the reverse equatorial plasma fountain during night-time has been made using images obtained by an All Sky Imaging Fabry-Perot Spectrometer observing the OI 630.0 nm airglow emission line from the thermosphere; the intensity of this line emission is directly related to the F-region plasma densities during night-time. From the identifiable features when the enhanced airglow emitting region moves overhead and when it completely leaves the field-of-view, the equatorwards velocity of the EIA has been estimated to be ~150 km/h at the latitude of the measurements (Mt Abu, 20°20′ dip latitude, India). Lower limits for the latitudinal and longitudinal extents of the EIA crest have each been inferred to be 6°.     

Neighbor-based Properties of Some Orderings of Two-dimensional Space

An ordering of a two-dimensional matrix assigns consecutive integers to the cells in that matrix. This paper evaluates such orderings by concentrating on the differences between each cell's order key and the keys of its spatial neighbors. In all, ten systematically generated orderings and two hundred random trials from a newly defined class of orderings are compared. The row-by-row (raster) ordering often used in remote sensing and in matrix ordering within computer programs minimizes the mean absolute difference, the root-mean-squared difference (and hence the Geary statistic), and the mean maximum absolute difference for both 8-by-8 and 256-by-256 matrices; of the quadrant-recursive (“quadtree-compatible”) orderings examined, the Morton order had the lowest values for both mean absolute difference measures, whereas the Hilbert order had the lowest root-mean-squared neighbor difference. The Morton order has the overall minimum value for the Moran statistic. Heuristic search procedures applied to the 8-by-8 case found orderings which had considerably “better” values for these statistics (higher for Moran; lower for the others) than did any of the above, suggesting that it will be possible to define new systematic orderings with better scores than any ordering currently in the literature.     

Morphological Characteristics of Healthy and Osteoarthritic Joint Surfaces in Archaeological Skeletons

Osteoarthritis is a major health concern in living populations, as well as being one of the most common pathological lesions identified in the archaeological record. The aetiology of the disease remains unclear, with a multi‐factorial influence of physical strain, age, genetics, and obesity. Previous studies have identified a relationship between the presence of knee osteoarthritis on the distal femoral joint and the morphology of the intercondylar notch, patellar groove, and medial condyle. The current study expands this research to investigate the relationship between distal femoral, distal humeral, and proximal ulnar joint morphology and osteoarthritis with 3D shape analysis techniques. These methods provide a more detailed analysis of joint morphology in order to determine any relationship between 3D shape and osteoarthritis. The results indicate a complex relationship between joint shape and knee osteoarthritis, with eburnated right femora showing a statistically significant association. The shapes associated with eburnated or affected femoral joints can be explained by osteophyte development, and therefore likely represent systematic shape changes and not a particular joint shape predisposing individuals to the condition. There was no identifiable relationship found in the proximal ulna or distal humerus, indicating that joint shape is unlikely to influence the development of the condition in the elbow joint and that any shape changes produced by osteoarthritis are not systematic or quantifiable. The joints analysed in this study were highly influenced by asymmetry, sexual dimorphism, and allometry, resulting in a small sample size of affected joints in many datasets. Further analyses of large skeletal samples are needed to more thoroughly investigate the possible relationship of distal femoral joint shape and osteoarthritis. Copyright © 2013 John Wiley & Sons, Ltd.     

Experimental Study of a Structure Under Stress Pulse Simulating Vertical Ground Motion

This article is an attempt to study the effects of a stress pulse simulating strong vertical excitation, particularly at the first steps of the mode of propagation. The structural model represents a two-story single column, having two pairs of cantilever beams on either side. The study is carried out by means of the experimental method of caustics. The areas of maximum stress concentration, as well as the wave front direction within the horizontal elements of the structure, are determined. The influence of the wave and the reflected effects on the top of the column are also studied. The experimental results are compared with the corresponding results obtained by finite element analysis. The results could be used for the development of rules for the effects of the vertical component.