A Computational Method for Market Area Analysis on a Network

This paper shows a computational method for market area analysis assuming that stores and consumers are distributed over a network and the distance between two points on the network is given by the route distance. First, we consider five basic questions often raised in market area analysis, and show a general method, called the network transformation method, that gives an intuitive way of looking at computational methods for solving these questions. Second, assuming that consumers follow the Huff model, we consider four questions concerning market area delineation and market potential often discussed in market area analysis in practice. We show that the network transformation method is also useful to develop computational methods for solving these questions. One of the notable results is that market area delineation of the Huff model (which is analytically difficult to obtain on a plane) can be exactly obtained on a network.     

SANET: A Toolbox for Spatial Analysis on a Network

This article shows a geographical information systems (GIS)-based toolbox for analyzing spatial phenomena that occur on a network (e.g., traffic accidents) or almost along a network (e.g., fast-food stores in a downtown). The toolbox contains 13 tools: random point generation on a network, the Voronoi diagram, the K -function and cross K -function methods, the unconditional and conditional nearest-neighbor distance methods, the Hull model, and preprocessing tools. The article also shows a few actual analyses carried out with these tools.     

An Extended K Function Method for Analyzing Distributions of Polygons with GIS

The objective of this paper is to develop a K function method for analyzing distributions of polygon-like entities in the real world by extending Ripley’s K function method. Many empirical studies using the K function method assume that entities are represented by points. If entities are small enough in comparison with a study area, this approximation may be acceptable. If not, polygon-like entities may not be approximated by points. To deal with polygon-like entities, this paper develops a K function method for analyzing distributions of polygons. First, the paper shows a method for extending the local K function of points to that of polygons. Second, the paper compares the result obtained from the K function of polygons with that of the points representing the polygons and shows a distinctive difference. Third, the paper formulates the cross K function method of polygons to analyze the relationship between two distributions of polygons of different kinds. Fourth, the paper implements the methods in GIS. Last, the paper applies the cross K function method of polygons to actual distributions of buildings of different uses in Aoyama, Tokyo.     

An Empirical Comparison of Edge Effect Correction Methods Applied to K‐function Analysis

This paper explores various edge correction methods for K‐function analysis via Monte Carlo simulation. The correction methods discussed here are Ripley's circumference correction, a toroidal correction, and a guard area correction. First, simulation envelopes for a random point pattern are constructed for each edge correction method. Then statistical powers of these envelopes are analyzed in terms of the probability of detecting clustering and regularity in simulated clustering/regularity patterns. In addition to the K‐function, K(h), determined for individual distances, h, an overall statistic k is also examined. A major finding of this paper is that the K‐function method adjusted by either the Ripley or toroidal edge correction method is more powerful than what is not adjusted or adjusted by the guard area method. Another is that the overall statistic k outperforms the individual K(h) across almost the entire range of potential distances h.     

Statistical Methods for Evaluating the Geometrical Hierarchy of a Network

The objective of this paper is to present statistical methods for evaluating the geometrical hierarchy of a network in comparison with a random hierarchy network. First, the random hierarchy network is explicitly formulated by four stochastic processes in which line segments or lines, which represent roads, are randomly placed and their placement is independent of their ranks. Second, under these stochastic processes, this paper derives the expected value and variance of i) the number of intersections between roads of different ranks; and ii) the distance from an arbitrary point to the nearest highest-ranked road through two kinds of routes. Using these expected values, the intersection index and the detour index are proposed, and it is shown that these indicators are useful for evaluating the geometrical hierarchy of a network. As calculation of these indices is laborious, an efficient computational method is developed, and its application to an actual example is described.     

Analysis of a Distribution of Point Events Using the Network‐Based Quadrat Method

This study proposes a new quadrat method that can be applied to the study of point distributions in a network space. While the conventional planar quadrat method remains one of the most fundamental spatial analytical methods on a two‐dimensional plane, its quadrats are usually identified by regular, square grids. However, assuming that they are observed along a network, points in a single quadrat are not necessarily close to each other in terms of their network distance. Using planar quadrats in such cases may distort the representation of the distribution pattern of points on a network. The network‐based units used in this article, on the other hand, consist of subsets of the actual network, providing more accurate aggregation of the data points along the network. The performance of the network‐based quadrat method is compared with that of the conventional quadrat method through a case study on a point distribution on a network. The χ² statistic and Moran's I statistic of the two quadrat types indicate that (1) the conventional planar quadrat method tends to overestimate the overall degree of dispersion and (2) the network‐based quadrat method derives a more accurate estimate on the local similarity. The article also performs sensitivity analysis on network and planar quadrats across different scales and with different spatial arrangements, in which the abovementioned statistical tendencies are also confirmed.     

DETECTING AND QUANTIFYING HEAT TREATMENT OF FLINT AND OTHER SILICA ROCKS: A NEW NON‐DESTRUCTIVE METHOD APPLIED TO HEAT‐TREATED FLINT FROM THE NEOLITHIC CHASSEY CULTURE,SOUTHERN FRANCE

Heat treatment of lithic raw material is known from the Middle Stone Age to the Neolithic. These findings require archaeometric techniques and methods for detecting the heat‐induced effects within lithic artefacts. However, the existing methods are often cost‐intensive and time‐consuming, and most of them are destructive. Here, we present a new method using the infrared spectroscopic measurement of the strength of H‐bonds formed between surface silanole groups (SiOH) and H₂O molecules held in open pores of the samples. The reduction of H‐bond strength in chalcedony is shown to be strongly correlated with the loss of open pores induced by heat treatment. Hence, the method is based on measuring one of the transformations aimed for by the instigators of the heat treatment: the reduction of porosity that modifies the rock's mechanical properties. A first application to heat‐treated material from the Neolithic Chassey culture (southern France) shows that flint was heated to temperatures between 200°C and 250°C in this period. This has important implications for the study of the procedures used and the heating environments. Our new method is non‐destructive, rapid, cost‐effective and allows for detection of the used annealing temperatures.     

Chemical Weathering of Detrital Sediments in the Taklamakan Desert,Northwestern China

Based on the analysis of major‐element compositions of detrital sediments from the Taklamakan Desert of northwestern China, this paper aims to study chemical weathering in a hyper‐arid desert environment. The major‐element compositions are basically similar to the Upper Continental Crust but show a clear enrichment of CaO and depletion of Na₂O and K₂O, indicating the enrichment of carbonates and the decomposition of sodium and potassium silicates. The indexes of chemical alteration are relatively low and correlate negatively with the content of Na₂O, implying that the degree of chemical weathering is weak and mainly controlled by the weathering of sodium feldspars. An A‐CN‐K model demonstrates that the detrital sediments from the Taklamakan Desert have a high homogeneity in the trend of chemical weathering. They are weathered less than sands and soil in many other Chinese deserts, and also less than similar detrital sediments in many other countries. This evidence suggests a low degree of mineralogical maturity in the Taklamakan Desert. The aeolian sediments of different ages have similar indexes of chemical weathering, suggesting that the degree of chemical weathering was consistent in the Taklamakan Desert throughout the period of aeolian deposition. The low degree of chemical weathering is caused principally by extreme aridity, rapid rejuvenation of detrital sediments associated with strong aeolian processes, and an intensive input of fluvial deposits, as well as a lack of vegetation. Due to the high concentration of erodible minerals, the desert is quite vulnerable to soil erosion and land degradation.     

Topic Modeling and Text Analysis for Qualitative Policy Research

This paper contributes to a critical methodological discussion that has direct ramifications for policy studies: how computational methods can be concretely incorporated into existing processes of textual analysis and interpretation without compromising scientific integrity. We focus on the computational method of topic modeling and investigate how it interacts with two larger families of qualitative methods: content and classification methods characterized by interest in words as communication units and discourse and representation methods characterized by interest in the meaning of communicative acts. Based on analysis of recent academic publications that have used topic modeling for textual analysis, our findings show that different mixed‐method research designs are appropriate when combining topic modeling with the two groups of methods. Our main concluding argument is that topic modeling enables scholars to apply policy theories and concepts to much larger sets of data. That said, the use of computational methods requires genuine understanding of these techniques to obtain substantially meaningful results. We encourage policy scholars to reflect carefully on methodological issues, and offer a simple heuristic to help identify and address critical points when designing a study using topic modeling.     

Experimental determination of CePO4 and YPO4 solubilities in H2O–NaF at 800°C and 1 GPa: implications for rare earth element transport in high‐grade metamorphic fluids

Monazite (CePO₄) and xenotime (YPO₄) are important accessory minerals in metasediments. They host significant rare earth elements (REE) and are useful for geochronology and geothermometry, so it is essential to understand their behavior during the metasomatic processes that attend high‐grade metamorphism. It has been proposed that F‐bearing fluids enhance solubility and mobility of REE and Y during high‐grade metamorphism. We assessed this possibility by determining the solubility of synthetic CePO₄ and YPO₄ crystals in H₂O–NaF fluids at 800°C and 1 GPa. Experiments used hydrothermal piston‐cylinder and weight‐loss methods. Compared to the low solubilities of CePO₄ and YPO₄ in pure H₂O (0.04 ± 0.04 and 0.25 ± 0.04 millimolal, respectively), our results indicate an enormous increase in the solubility of both phosphates with increasing NaF concentration in H₂O: CePO₄ solubility reaches 0.97 molal in 20 mol.% NaF, and YPO₄ shows an even stronger solubility enhancement to 0.45 molal in only 10 mol.% NaF. The greatest relative solubility increases occur at the lowest NaF concentration. The solubilities of CePO₄ and YPO₄ show similar quadratic dependence on NaF, consistent with possible dissolution reactions of: CePO₄ + 2NaF =  CeF₂⁺ + Na₂PO₄^? and YPO₄ + 2NaF = YF₂⁺ + Na₂PO₄^?. Solubilities of both REE phosphates are significantly greater in NaF than in NaCl at equivalent salt concentration. A fluid with 10 mol.% NaCl and multiply saturated with fluorite, CePO₄, and YPO₄ would contain 1.7 millimolal Ce and 3.3 millimolal Y, values that are respectively 2.1–2.4 times greater than in NaCl‐H₂O alone. The results indicate that Y, and by extension heavy rare earth elements (HREE), can be fractionated from LREE in fluorine‐bearing saline brines which may accompany granulite‐facies metamorphism. The new data support previous indications that REE/Y mobility at these conditions is enhanced by complexing with F in the aqueous phase.     

Changes in chemical composition caused by water–rock interactions across a strike‐slip fault zone: case study of the Atera Fault,Central Japan

In some cases, water–rock interactions in fault zones can affect radionuclide migration. Here, we analyzed the chemical compositions of well‐exposed fault rocks from the strike‐slip Atera Fault, Central Japan, in order to understand the variability and behavior of major and selected trace elements. The fault zone has a 1.2‐m‐wide, smectite‐rich fault core and paired damage zones that developed within welded tuff on one side of the core and within granite on the other side. The 30‐cm‐wide, kaolinite‐rich fault gouge is developed in granite cataclasite, and it shows indications of the latest fault activity, while the 1.2‐m‐wide fault core appears to be older. Hydrogen and oxygen isotope ratios in the clay‐rich fault gouges, and carbon and oxygen isotope ratios in carbonates indicate that the two major clay‐rich zones formed in bedrock near the surface, consistent with observed deformation structures. Based on chemical analyses, we identified (1) a slight depletion in SiO₂, Na₂O, K₂O, and light rare earth elements at the edges of the 1.2‐m‐wide fault core, (2) a clear depletion in SiO₂, Na₂O, K₂O, and all rare earth elements except Eu in the 30‐cm‐wide fault gouge, and (3) an increase in CaO, MnO, and heavy rare earth elements across the entire 1.2‐m‐wide fault core. Findings (1) and (2) reflect water–rock interactions in the 1.2‐m‐wide fault core and in the 30‐cm‐wide fault gouge that resulted in the formation of smectite and kaolinite. Finding (3) reflects carbonate precipitation caused by the addition of basalt fragments from a nearby site to the 1.2‐m‐wide fault core during faulting, and subsequent sorption reactions of heavy rare earth elements via processes such as complexation with the carbonates.     

INVESTIGATING SEASONALITY AND SEASON OF BIRTH IN PAST HERDS: A REFERENCE SET OF SHEEP ENAMEL STABLE OXYGEN ISOTOPE RATIOS

Intra‐tooth sequential analysis of enamel δ¹⁸O is currently used to investigate birth seasonality in past animal populations, offering new insights into seasonal availability of animal resources, herd management and seasonality of site occupation. Reference data sets are still required to address two major difficulties: (1) that inter‐individual variability in the record of the seasonal cycle is affected by tooth size; and (2) that the season of birth cannot be directly estimated from the timing of tooth growth, because of a delay in enamel mineralization. We present a data set acquired on the lower second molar of 10 modern sheep from Rousay (Orkney) born within a few weeks of each other in April/May and submitted to the same environmental conditions until death. All sheep have recorded a sinusoidal pattern of δ¹⁸O variation spanning approximately a year. From the difference between the expected and the measured time sequence, the delay of enamel mineralization is estimated to be 5–6 months. The data set is then described using a model mainly based on a cosine function. The period, corresponding to the length of the M2 crown formed over a year, averaged 35.8 mm. A very slight variation of tooth growth rate with time and no attenuation of the isotopic signal towards the cervical margin of the crown could be detected in this data set. The lowest δ¹⁸O values, corresponding to the sheep's first winter, were tracked at a distance from the enamel/root junction that varied between 23.0 and 30.3 mm (x_min mean = 27.6 mm); the highest δ¹⁸O values, corresponding to the sheep's second summer, were between 6.3 and 11.6 mm (x_max mean = 9.9 mm). Most of the variability can be attributed to tooth size. When normalized on the period, x_min and x_max are 0.28 (± 0.05) and 0.78 (± 0.05) on average, meaning that the Rousay sheep have recorded the minimum and maximum δ¹⁸O values on average at 78% and 28%, respectively, of the end of the periodic cycle recorded in the second molar.     

A Minimax Method for Finding the k Best “Differentiated” Paths

In real-world applications, the k-shortest-paths between a pair of nodes on a network will often be slight variations of one another. This could be a problem for many path-based models, particularly those on capacitated networks where different routing alternatives are needed that are less likely to encounter the same capacity constraints. This paper develops a method to solve for k differentiated paths that are relatively short and yet relatively different from one another, but not necessarily disjoint. Our method utilizes the sum of a path's distance plus some fraction of its shared distance with each other path. A minimax algorithm is used to select the path whose largest sum of length, plus shared length vis-à-vis each previously selected path, is as small as possible. We present computational results for the Chinese railway system, comparing the paths generated by a standard k-shortest-path algorithm with those from our new model.     

Evaluation of Quantitative XRF Analysis Applied to Determine Cobalt Sources in Chinese Blue‐and‐White Porcelain

A method using the ratios between MnO, Fe₂O₃ and CoO to differentiate the cobalt sources for Chinese blue‐and‐white porcelain was developed in Oxford in the 1950s using X‐ray fluorescence (XRF) analysis directly on the glaze. In this paper, six blue‐and‐white porcelain sherds from the Luomaqiao kiln were analysed by XRF on the glaze and by scanning electron microscopy with energy‐dispersive spectrometry (SEM‐EDS) in cross‐section. The ratios between MnO, Fe₂O₃ and CoO calculated by quantitative XRF and EDS analyses are different. The analysis depths for MnO, Fe₂O₃ and CoO are < 60 μm by XRF analysis. However, the average glaze thickness of samples is > 400 μm, and the MnO, Fe₂O₃ and CoO mainly remain in the lower layer of the glaze, which is beyond the analysis depths of XRF analysis. The limitations of major and minor quantitative analyses for differentiating cobalt sources are discussed.     

The Chemical Composition and Production Area of Early Western Zhou Proto‐Porcelain Unearthed from Yejiashan Cemetery,Suizhou, China

The bodies and glazes of 27 early Western Zhou proto‐porcelain samples from Yejiashan cemetery, Hubei Province, were analysed using LA‐ICP–AES, SEM, XRD, a thermal expansion instrument and other analytical methods. The results indicated that the bodies of all samples were characterized by high silicon and low aluminium, and were made with porcelain stone raw materials found in the south of China. The glazes are typical of high‐temperature calcium glazes of the CaO (MgO) – K₂O (Na₂O) – Al₂O₃ – SiO₂ series, with relatively high Mn and P content, which was probably caused by the addition of plant ashes. The physical properties and phase compositions of Yejiashan proto‐porcelain show that firing processes were still in the early stages of development in ancient China. Multivariate statistical analyses indicated that Yejiashan proto‐porcelain might have come from the Deqing area, in Zhejiang Province. These results provide new archaeological evidence for research on issues related to material flow in the Western Zhou dynasty.     

Fluid sinks within the earth's crust

The Urach 3 research borehole in south‐west (SW) Germany has been drilled through the sedimentary cover, and the gneisses of the Variscian crystalline basement at 1600 m below the surface (Black Forest basement) has been reached. An additional 2800 m has been drilled through the fractured crystalline rocks, and the borehole has been used for a number of hydraulic tests in the context of a ‘hot‐dry rock’ (HDR) project exploring for geothermal energy. The fracture system of the basement is saturated with a NaCl brine with about 70 g L^?1 dissolved solids. Water table measurements in the borehole cover a period of 13 years of observation, during which the water table continuously dropped and did not reach a steady‐state level. This unique set of data shows that the hydraulic potential decreases with depth, causing a continuous flow of fluid to the deeper parts of the upper continental crust. The potential decrease and the associated downward migration of fluid is an evidence for the progress of water (H₂O)‐consuming reactions in the crystalline rocks. Computed stability relations among relevant phases at the pressure temperature (PT) conditions in the fracture system and documented fossil fracture coatings in granites and gneisses suggest that the prime candidate for the H₂O‐consuming reaction is the zeolitization of feldspar. The potential of the gneisses to chemically bind H₂O matches the estimated amount of migrating H₂O.     

Fractal analysis of veins in Permian carbonate rocks in the Lingtanchang anticline,western China

Statistical analysis of the thickness distribution of veins in the Lingtanchang structure, southern Sichuan basin, western China, indicates that vein thickness conforms to fractal character and a power‐law distribution, whereas various distributions of veins are indicated by both the spacing distribution and the C_v values. According to geometry and structure, the veins in the Lingtanchang structure can be divided into confined and through‐going veins. The statistical analyses show that confined intralayer veins are consistent with a power‐law distribution in thickness, with D_t values of 1.1–1.7 and a log‐normal distribution in spacing with C_v values of 0.8–0.9. The confined intra‐ to interlayer veins show D_t values of 1.0–1.3 and an exponential distribution in spacing, with C_v values of 0.9–1.0, indicating an unconnected vein network with weak ability for paleofluid flow. However, the through‐going veins show the lowest D_t values of 0.6–0.8 with a power‐law distribution in thickness and power‐law to exponential distribution in spacing with C_v values of 1.5–3.2. Differences in spacing distribution and in the thickness of veins can be explained by different stages of vein growth from confined to through‐going veins. Such processes are dominant with percolating cluster models, which significantly controls spatial distribution of veins and paleofluid flow, and therefore the reservoir conditions in the southern Sichuan basin.     

RESEARCH ON THE PIGMENTS FROM PAINTED CERAMICS EXCAVATED FROM THE YANGQIAOPAN TOMBS OF THE LATE HAN DYNASTY (48 BC – AD 25)

The analysis of pigments on painted ceramics excavated from the Yangqiaopan Tombs of the late Western Han Dynasty was undertaken using optical microscopy (OM), micro‐Raman spectroscopy (μ‐RS), scanning electron microscopy with energy‐dispersive X‐ray spectrometry (SEM–EDS), X‐ray diffraction (XRD) and Fourier‐transform infrared spectroscopy spectra (FTIR). The pigments were identified as red lead (Pb₃O₄), carbon (C), malachite [Cu₂CO₃(OH)₂], Chinese purple (BaCuSi₂O₆) and illite {[K,H₃O]Al₂Si₃AlO₁₀(OH)₂}. Fibrous materials were observed in some pigment samples. When observed by SEM, one showed a large amount of fibre in solidified gum, which indicated that gum of ramie could have been used as the binding medium to make the pigment particles adhere together. These results provide significant insights into the characteristics of these pigments in the Qin and Han Dynasties.     

Freezing and melting behaviors of H2O‐NaCl‐CaCl2 solutions in fused silica capillaries and glass‐sandwiched films: implications for fluid inclusion studies

Fluid inclusions of the H₂O‐NaCl‐CaCl₂ system are notorious for their metastable behavior during cooling and heating processes, which can render microthermometric measurement impossible or difficult and interpretation of the results ambiguous. This study addresses these problems through detailed microscopic examination of synthetic solutions during cooling and warming runs, development of methods to enhance nucleation of hydrates, and comparison of microthermometric results with different degrees of metastability with values predicted for stable conditions. Synthetic H₂O‐NaCl‐CaCl₂ solutions with different NaCl/(NaCl + CaCl₂) ratios were prepared and loaded in fused silica capillaries and glass‐sandwiched films for microthermometric studies; pure solutions were used with the capillaries to simulate fluid inclusions, whereas alumina powder was added in the solutions to facilitate ice and hydrate crystallization in the sandwiched samples. The phase changes observed and the microthermometric data obtained in this study have led to the following conclusions that have important implications for fluid inclusion studies: (i) most H₂O‐NaCl‐CaCl₂ inclusions that appear to be completely frozen in the first cooling run to ?185°C actually contain large amounts of residual solution, as also reported in some previous studies; (ii) inability of H₂O‐NaCl‐CaCl₂ inclusions to freeze completely may be related to their composition (low NaCl/(NaCl + CaCl₂) ratios) and lack of solid particles; (iii) crystallization of hydrates, which is important for cryogenic Raman spectroscopic studies of fluid inclusion composition, can be greatly enhanced by finding an optimum combination of cooling and warming rates and temperatures; and (iv) even if an inclusion is not completely frozen, the melting temperatures of hydrohalite and ice are still valid for estimating the fluid composition.