An Approximation for the Rank Adjacency Statistic for Spatial Clustering with Sparse Data

The rank adjacency statistic D provides a simple method to assess regional clustering. It is defined as the weighted average absolute difference in ranks of the data, taken over all possible pairs of adjacent regions. In this paper the usual normal approximation to the D statistic is found to give inaccurate results if the data are sparse and some regions have tied ranks. Adjusted formulae for the moments of D that allow for the existence of ties are derived. An example of analyses of sparse mortality data (with many regions having no deaths, and hence tied ranks) showed satisfactory agreement between the adjusted formulae and the empirical distribution of the D statistic. We conclude that the D statistic, when used with adjusted moments, provides a valid approximate method to evaluate spatial clustering, even in sparse data situations.     

Geographic information system‐based edge effect correction for Ripley's K‐function under irregular boundaries

Ripley's K‐function is a test to detect geographically distributed patterns occurring across spatial scales. Initially, it assumed infinitely continuous planar space, but in reality, any geographic distribution occurs in a bounded region. Hence, the edge problem must be solved in the application of Ripley's K‐function. Traditionally, three basic edge correction methods were designed for regular study plots because of simplified geometric computation: the Ripley circumference, buffer zone, and toroidal methods. For an irregular‐shaped study region, a geographic information system (GIS) is needed to support geometric calculation of complex shapes. The Ripley circumference method was originally implemented by Haase and has been modified into a Python program in a GIS environment via Monte Carlo simulation (hereafter, the Ripley–Haase and Ripley–GIS methods). The results show that in terms of the statistical powers of clustering detection for irregular boundaries, the Ripley–GIS method is the most stable, followed by the buffer zone, toroidal, and Ripley–Haase methods. After edge effects of irregular boundaries have been eliminated, Ripley's K‐function is used to estimate the degree of spatial clustering of cities in a given territory, and in this paper, we demonstrate that by reference to the relationship between urban spatial structure and economic growth in China.     

Power of the Rank Adjacency Statistic to Detect Spatial Clustering in a Small Number of Regions

The rank adjacency statistic D is a statistical method for assessing spatial autocorrelation or clustering of geographical data. It was originally proposed for summarizing the geographical patterns of cancer data in Scotland (IARC 1985). In this paper, we investigate the power of the rank adjacency statistic to detect spatial clustering when a small number of regions is involved. The investigations were carried out using Monte Carlo simulations, which involved generating patterned/clustered values and computing the power with which the D statistic would detect it. To investigate the effects of region shapes, structure of the regions, and definition of weights, simulations were carried out using two different region shapes, binary and nonhinary weights, and three different lattice structures. The results indicate that in the typical example of considering Canadian total mortality at the electoral district level, the D statistic had adequate power to detect general spatial autocorrelation in twenty‐five or more regions. There was an inverse relationship between power and the level of connectedness of the regions, which depends on the weighting function, shape, and arrangement of the regions. The power of the D statistic was also found to compare favorably with that of Moran's I statistic.     

The K‐Function Method on a Network and Its Computational Implementation

This paper proposes two statistical methods, called the network K‐function method and the network cross K‐function method, for analyzing the distribution of points on a network. First, by extending the ordinary K‐function method defined on a homogeneous infinite plane with the Euclidean distance, the paper formulates the K‐function method and the cross K‐function method on a finite irregular network with the shortest‐path distance. Second, the paper shows advantages of the network K‐function methods, such as that the network K‐function methods can deal with spatial point processes on a street network in a small district, and that they can exactly take the boundary effect into account. Third, the paper develops the computational implementation of the network K‐functions, and shows that the computational order of the K‐function method is O(n²_Q log n_Q) and that of the network cross K‐function is O(n_Q log U3Q), where n_Q is the number of nodes of a network.     

New Statistical Approaches to Intra‐individual Isotopic Analysis and Modelling of Birth Seasonality in Studies of Herd Animals

This paper introduces improved methods for statistically assessing birth seasonality and intra‐annual variation in δ¹⁸O from faunal tooth enamel. The first method estimates input parameters for use with a previously developed parametric approach by C. Tornero et al. The second method uses a non‐parametric clustering procedure to group individuals with similar time‐series data and estimate birth seasonality. This method was successful in analysing data from a modern sample with known season of birth, as well as two heterogeneous archaeological data sets. Modelling indicates that the non‐parametric approach estimates birth seasonality more successfully than the parametric method when less of the tooth row is preserved. The new approach offers a high level of statistical rigour and flexibility in dealing with the time‐series data produced through intra‐individual sampling in isotopic analysis.     

WROUGHT IRON FROM THE USS MONITOR: MINERALOGY,PETROLOGY AND METALLOGRAPHY*

The metal and its slag inclusions from the USS Monitor are mineralogical and geological artefacts of a vessel that has catalysed and documented the technology of maritime construction and warfare since 1862. Petrological study of a wrought iron disc from the hull of the Monitor reveals low‐carbon, high‐phosphorus ferrite with 4.8 vol% silicate slag, which includes phosphoran olivine, glass, wüstite and a silica polymorph. The sample, although made at the height of wrought iron manufacture, is of only mediocre quality and has a mineralogy, petrology and metallography that reflect the latter stages of puddling, rolling, annealing and 140 years of corrosion.     

The p‐Regions Problem. p‐区域问题

The p‐regions problem involves the aggregation or clustering of n small areas into p spatially contiguous regions while optimizing some criteria. The main objective of this article is to explore possible avenues for formulating this problem as a mixed integer‐programming (MIP) problem. The critical issue in formulating this problem is to ensure that each region is a spatially contiguous cluster of small areas. We introduce three MIP models for solving the p regions problem. Each model minimizes the sum of dissimilarities between all pairs of areas within each region while guaranteeing contiguity. Three strategies designed to ensure contiguity are presented: (1) an adaptation of the Miller, Tucker, and Zemlin tour‐breaking constraints developed for the traveling salesman problem; (2) the use of ordered‐area assignment variables based upon an extension of an approach by Cova and Church for the geographical site design problem; and (3) the use of flow constraints based upon an extension of work by Shirabe. We test the efficacy of each formulation as well as specify a strategy to reduce overall problem size.     

THE MAX‐P‐REGIONS PROBLEM*

ABSTRACT In this paper, we introduce a new spatially constrained clustering problem called the max‐p ‐regions problem. It involves the clustering of a set of geographic areas into the maximum number of homogeneous regions such that the value of a spatially extensive regional attribute is above a predefined threshold value. We formulate the max‐p ‐regions problem as a mixed integer programming (MIP) problem, and propose a heuristic solution.     

MEAN SHIFT: A NON‐PARAMETRIC ALGORITHM FOR THE SEGMENTATION OF ANOMALIES IN GEOPHYSICAL IMAGES OBTAINED FROM MAGNETIC PROSPECTION DATA

This paper studies the applicability of the Mean Shift algorithm as support in interpreting geophysical images produced, on this occasion, from magnetic prospection data. The data obtained from a magnetic survey carried out in Gilena (Seville province, Spain) by the La Rábida Archaeophysics Group will be used for the research. Its applicability is illustrated by comparing, on the one hand, some reduction‐to‐pole algorithms and on the other, the (well‐known) k‐means algorithm. Finally, the paper shows the results obtained by applying the Mean Shift algorithm as an alternative method to ‘unsupervised clustering’ of anomalies that appear in images obtained from geophysical data, in which the a priori knowledge of the number of classes is difficult or impossible.     

PATHS IN TRANSNATIONAL TIME-SPACE: REPRESENTING MOBILITY BIOGRAPHIES OF YOUNG SWEDES

This article sets out to capture and describe individual transnational mobility from a long‐term, biographical perspective. The purpose is to discuss the use of a time‐geographical form of notation to represent people's transnational mobility as paths in time and space, and to demonstrate how such representations can contribute to explaining some of the dynamics of longdistance mobility. An advantage of using time‐space paths is that several aspects of an individual's travel biography can be represented in a single image: intensity and extensity are immediately evident, and the temporal and spatial relationships between the various mobility actions are made visible. Using data describing all transnational trips taken during childhood and adolescence by sixty‐two Swedish youth with different backgrounds, three aspects of how trajectories develop over time are discussed in more detail. The first concerns overall change in travel pattern with time. A dominant pattern of increase in travel with increasing age is observed, indicating the importance of further investigating how travel behaviour is related to experience and life‐course transitions. Second, sequential relationships between migration and temporary mobility are examined. In spite of the relatively small number of respondents, a wide range of such relationships are disclosed in the material. Third, regularity and repetition in long‐distance travel patterns is discussed as an increasingly important aspect of contemporary transnational mobility. Among these young people, highly regular travel is often motivated by enduring long‐distance social relationships, but is also generated by leisure or holiday travel alone.     

The southern highlands from Gourock

The British Mission to Uganda in 1893. By the late Sir Gerald Portal, K.C.M.G., C.B., the British Commissioner. Edited, with a Memoir, by Rennell Rodd, C.M.G. With the Diary of the late Captain Raymond Portal, and an Introduction by Lord Cromer, G.C.M.G. Illustrated from photographs by Colonel Rhodes. London: Edward Arnold, 1894. Pp. 351 and map. Price 21s.

Durch Massailand zur Nilquelle. Beisen und Forschungen der Massai‐Expedition des Deutschen Antisklavereikomite in den Jahren 1891–1S93. Von Dr. Oscar Baumann. Berlin. Geographische Verlagshandlung, Dietrich Reimer, 1894. Pp. 377, Index, Map, and 27 Plates. 140 Illustrations in text.

Die Liparischen Inseln. Erstes Heft, Vulcario : Zweites Heft, Salina. Prag: Heinrich Mercy, 1893.

Polar Gleams : An Account of a Voyage on the Yacht ” Blencathra.” By Helen Peel. With a Preface by the Marquis of Dufferin, and Contributions by Captain Joseph Wiggins and Frederick G. Jackson. London : Edward Arnold, 1894. Pp. 211. Price 15s.

Die Beise S.M. Schiffes ” Zrinyi “ nach Ost‐Asien. (Yang‐tse‐kiang und Gelbes Meer) 1890–91. Verfasst im Auftrage des k. undk. Reichs‐Kriegsministeriuins Marine‐Section, unter Zugrundelegung der Berichte des k. und k. Schiffs‐commandos, und ergänzt nach Consularberichten und anderen authentischen Quellen. Von Jerolim, Freiherrn von Benko, k. und k. Fregatten‐Capitän d. R. Mit einer Keiseskizze und acht lithographirten Tafeln. Wien : Carl Gerold's Sohn, 1894. Pp. xi + 439.

Andalusien. Eine Winterreise durch Südspanien und ein Ausflug nach Tanger. Von Ernst von Hesse‐Wartegg. Leipzig : Verlag von Carl Eeissner, 1894. Pp. viii + 443.

Some Salient Points in the Science of the Earth. By Sir J. William Dawson, C.M.G., LL.D., etc. With Forty‐six Illustrations. London: Hodder and Stoughton, 1893. Pp. x + 499. Price 7s. 6d.

Life of General Sir Hope Grant, with Selections from his Correspondence. Edited by Henry Knollys, Colonel (H.P.) Royal Artillery, his former A.D.C. William Blackwood and Sons, 1894. Two volumes, pp. 359 and 362, with Index and Illustrations.

Rulers of India: Sir Thomas Munro and the British Settlement of the Madras Presidency. By John Bradsiiaw, M.A., LL.D., Inspector of Schools, Madras. Oxford : At the Clarendon Press, 1894. Pp. 233. Price 2s. 6d.

Japan ("The Story of the Nations” Series). By David Murray, Ph.D., LL.D. London : T. Fisher Unwin, 1894. Pp. v + 420. Price 5s.

Elementary Meteorology. By William Morris Davis, Professor of Physical Geography in Harvard College. Boston, U.S.A.: Ginn and Company, 1894. Pp. xii + 355. Price 10s. 6d.

Land Systems of Australasia. By William Epps, author of The People and the Land. London: Swan Sonnenschein and Co.; New York: Charles Scribner's Sons, 1894. Pp. 184.

Special Report on the Agricultural Resources of Canada. By Robert Wallace, F.L.S., F.E.S.B.

Scotch Tenant‐Farmers on the Agricultural Resources of Canada. The Eeports of Mr. John Steven and Mr. Alexander Fraser on their visit to Canada in 1893.

Canadian Agriculture. A Report of a Visit to the Dominion in 1893. By Professor James Long. London: 1894.

Le Père Huc et ses Critiques. Par Henri‐Ph. d'Orléans. Paris: Calman Lévy, 1893. Pp. 65.

Anson's Voyage round the World in the Years 1740, 1741, 1742, 1743, 1744. By Richard Walker, M.A., Chaplain of the Flag‐ship Centurion. London, Glasgow, and Dublin : Blackie and Son, Limited, 1894. Pp. 220. Price 1s. 4d.

The County Directory of Scotland (for 1893–1896), containing the Postal Addresses of Mansions and other Rural Residences in Scotland; their Occupants; nearest Telegraph Office and Distance;—also, the Postal and Telegraph Addresses of all Towns, Villages, etc. ; and various Information appertaining thereto. Postally edited by George Massie, General Post Office, Edinburgh. Proprietor and General Editor, Arthur Giles, F.R.S.G.S. Edinburgh : K. Grant and Son, 1894. Pp. xxx+ 1048.     

A Study Of The Firing Technique Of Pottery From Kaman‐Kalehöyük,Turkey, by Synchrotron Radiation‐Induced Fluorescence X‐Ray Absorption Near‐Edge Structure (Xanes) Analysis*

Fe K‐XANES spectra of a series of pottery sherds excavated from the archaeological site of Kaman‐Kalehöyük, Turkey, were measured to reveal the firing technique of the pottery. The analysis disclosed relationships among the chemical form of the iron, the firing conditions and the colour of the pottery. The pottery referred to as ‘Grey Ware’ found at this site was classified into two groups according to the chemical form of the iron. Also, it was revealed that the Iron Age pottery referred to as ‘Cream Ware’ was produced first under reducing conditions, and then fired under oxidizing conditions.     

CUERDA SECA CERAMICS FROM AL‐ANDALUS,ISLAMIC SPAIN AND PORTUGAL (10TH−12TH CENTURIES AD): INVESTIGATION WITH SEM–EDX AND CATHODOLUMINESCENCE*

Since little is known about the cuerda seca technique, our aim has been to complete an initial analysis of 11th‐century cuerda seca by studying fragments from the 10th century (Pechina, Almería) and the 12th century (Mértola and Almería), so as to establish the diachronic evolution of this technique. Characteristics specific to cuerda seca ceramic glazes were investigated using scanning electron microscopy (SEM) and quantitative chemical analysis with energy‐dispersive X‐ray spectrometry (EDX). The chemical compositions of the different‐coloured glazes (green, black, yellow and white) have given us valuable indications about the evolution of the technique. The opacification mode and the firing process were also investigated. With the help of cathodoluminescence (CL) and the study of modern ‘cuerda seca’ glazed ceramics, new hypotheses regarding the number of firing stages, taking into account glaze and paste transformations and their interactions, are put forward.     

Texts,topoi and the self: a reading of Alfredian spirituality*

Challenging the allegation that Alfred's spirituality as Asser presents it is no more than a string of textual fictions, this article outlines a context for understanding Alfred's spirituality as a functional process of living texts, or of ‘textualizing’ the self. The discussion first draws support for this view from the history of early medieval spirituality and then demonstrates the theme's relevance both to Asser's representation of Alfred and to the king's own writings. Attention is given especially to the congruence between Alfred's depiction in the Life and Gregory the Great's teachings on the ideal rector as propounded in the Pastoral Care, a text carefully read and famously translated by Alfred himself. The comparison suggests that the main spiritual models for Alfred's kingly piety may be understood to reside in, and to involve assimilation of, this work of Gregory, making it possible to conceptualize the king's self‐presentation in terms of a conscious project to ‘live’ Gregory's text by bringing the ideals of the Gregorian rector to life in his own person. Such an argument helps to explain Alfred's interest in Gregory, to account for his concern to translate the Pastoral Care, and to legitimize the predominant images associated with the king's spirituality as indicative of a kind of functional piety grounded in the reading of texts, rather than simply reflected, perhaps falsely, in Asser’s Life.     

A Note on the Extremities of Local Moran's Iis and Their Impact on Global Moran's I

By defining local Moran's I_i as a ratio of quadratic forms and making use of its overall additivity to match global Moran's I, we can identify spatial objects with a strong impact on global Moran's I. First, we concentrate on the spatial properties of local Moran's I_i expressed by the local linkage degree. Depending on whether we use the W- or C-coding of the spatial connectivity matrix, the variance of local Moran's I_i for a small local linkage degree will be either large or small. Note that spatial objects associated with a local Moran's I_i with a large variance affect the global statistic much more than spatial objects associated with a local Moran's I_i with a small variance. Counterintuitively, global Moran's I defined in the W-coding is most influenced by spatial objects with a small number of spatial neighbors. In contrast, spatial objects with a large number of spatial neighbors exert more impact on global Moran's I setup in the C-coding. Second, we investigate the impact of the empirical data on local Moran's I_i and show that local Moran's I_i will only be significant for extreme absolute residuals at and around the reference location. Clusters of average regression residuals cannot be detected by local Moran's I_i. Consequently, spatial cliques of extreme residuals contribute more to significance tests on global autocorrelation.     

The Material Nature of the Radiance of YHWH and its Theological Implications

Abstract

Kābôd-YHWH is a technical term designating the radiance of the god of Israel. Such a phenomenon is specifically identified in the Bible with three physical realities: volcanic lava, solar activity and molten metal. The antique representation of the sun as molten metal, and the volcanic symbolism of the furnace reveal that these three expressions of kābôd-YHWH are interrelated. Among them, it appears here that kābôd-YHWH refers first of all to molten metal. This introduces a fundamental difference between radiance, specifically related to YHWH through molten metal, and brilliance (and by extension glory, wealth, strength and vitality) of gods and mortals derived from properties of solid state metals. Beyond the status and powers of supreme deity conferred by this metallurgical radiance, identification of kābôd-YHWH as shapeless molten metal also clarifies the origin of one of the most singular characteristic of ancient Yahwism: the strict interdiction of figuration of the god.     

UBI SUNT MACELLA? THE CONTRIBUTION OF NON‐INVASIVE ARCHAEOLOGICAL SURVEY TO THE IDENTIFICATION AND STUDY OF ROMAN FOOD MARKETS

While the remains of the well‐preserved and excavated towns of Pompeii, Ostia and Herculaneum provide us with a fascinating impression of their once bustling economic life, the study of urban economic space requires a more extensive geographical and methodological framework. This paper investigates whether the systematic use of non‐invasive techniques at other, often neglected, urban sites can deliver a meaningful contribution to the study of Roman urbanism, especially by revealing previously unknown foci of commercial activity in the Roman city. To illustrate the effectiveness of certain non‐destructive strategies, including geophysical prospection and aerial survey, we focus on a specific type of market building that was quite common in the Roman world, the macellum. The case studies presented here demonstrate how non‐invasive archaeological investigation, often in combination with other topographic operations, can facilitate the identification of macella and enhance studies of economic architecture and space in Roman towns in Italy and the provinces.