Minimum-Cost Distances in Spatial Analysis

An axiomatic approach to distance is developed which focuses on those behavioral concepts of distance related to movement in space. In particular, spatial movement by behaving units is postulated to involve a choice from among some set of abstract trips in space, and implicitly, to involve the minimization of some relevant notion of trip costs. In this context, the relevant behavioral notion of distance in space is taken to be the minimum-cost distance generated by this choice process. These trip-cost concepts extend the classical notions of paths, path lengths, and shortest paths in metric spaces. Hence many of the analytical results of the paper involve extensions of classical shortest-path distance properties to minimum-cost distances. In addition to these extensions, a characterization theorem is given which specifies the possible functional relationships between trip costs and their associated path lengths. These relationships include most functional forms which are commonly employed in the literature.     

Shortest Distances in a Modified Transportation Network

Taking as the starting point an undirected source network and a set of possible new links that can be used to extend the source network, a method is proposed to determine, by simple inspection of a matrix tableau, all shortest distances in any extended network, without using a shortest path algorithm. In consequence, this method may be a useful tool for analyzing and judging network extensions. In particular, computation time can be saved in many complex network optimization methods that use shortest path algorithms. The computer experiments show that the method is feasible even when an extended network may differ from the source network by several dozens of branches.     

城市系统演化的复杂性研究

城市演化是由复杂多样的动力和主体推动的,受全球、国家和地方尺度的多重影响,表现出复杂的演化规律和特征。笔者认为城市系统演化模式与过程的研究需要发展一个基于复杂性理论的跨学科的分析框架。本文首先提出一个城市系统演化的概念模型,然后运用层次理论分析了城市系统演化的复杂相互作用,论述了城市系统演化的组成异质性、时空复杂性、决策复杂性等复杂性表征,最后讨论了城市系统演化的各种复杂规律。     

Shortest-Path Distances: An Axiomatic Approach

An axiomatic approach to distance is developed which focuses on those concepts of distance related to movement in space. The most fundamental types of such distances generally involve some notion of shortest paths between points, where the relevant concept of path length can be any additive attribute of paths (such as physical miles, hours spent in traveling, or gallons of fuel consumed). In particular, the shortest-path distance between any two points in space is here taken to be the greatest lower bound on all path lengths between these points. This notion of shortest-path distance is shown to be formally equivalent to a quasimetric, i.e., a distance which satisfies only the classical triangularity axiom for metrics. The main analysis of the paper focuses on the question of whether or not such shortest-path distances can actually be realized, i.e., on whether there exist shortest paths in space. The central result is to establish a general set of conditions under which such shortest paths always exist. In addition, a condition for the uniqueness of these paths is also established.     

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.     

Models of Space Searching in Urban Areas

City dwellers occasionally must seek jobs, dwellings, or particular services or goods. Two very different ways exist by which the individual may conduct such a search. Lacking prior information, the person may elect to visit perceived possible locations until an appropriate one is found. Alternatively, an address may first be ascertained and then visited by finding a path to it. Clearly, there is a substantial difference between these two methods in terms of the amount of spatial movement they require in order to satisfy the searcher's needs. In this paper, this difference is modeled for situations that vary in terms of the density of acceptable end points of the search, as well as in characteristics of the signs of these end points, their patterns, and the level of information with which the searcher may begin.     

Spatial Analysis in Physical Geography and the Challenge of Deterministic Uncertainty

The application of complex and nonlinear dynamical systems (NDS) theory in physical geography and geosciences has proceeded through several stages, and has recently entered a phase where field-testable hypotheses and historical or mechanistic explanations are being generated. However, there are some fundamental challenges. It seems clear that chaos and dynamical self-organization are present, and may be common in earth surface systems, and that these phenomena have spatial manifestations in the landscape. However, NDS theory and methods have been formulated primarily in the temporal domain and are typically ill-suited to real-world spatial data. Spatial analytical methods are not generally capable of distinguishing deterministic complexity and uncertainty from noise. Thus, the detection of the signals of complex deterministic dynamics in real landscapes and spatial data is a major challenge. Entropy-based methods of spatial analysis can be directly linked to nonlinear dynamics, and are at present the best available method to approach this problem. However, there is evidence in the spatial analysis literature suggesting that development of techniques to detect deterministic uncertainty is possible. Pending such a break-through, three general approaches are described, based on spatial analysis of chronosequences, the characteriziation of changes in spatial structure over time, and the spatial-domain testing of specific hypotheses relevant to deterministic uncertainty. Current trends generally suggest a shift in mathematical modeling and spatial analysis in physical geography away from traditional determinism toward approaches that incorporate locational, historical, and scale contingency.     

Investigating the Influence of Spatial and Temporal Granularities on Agent‐Based Modeling

Epidemic agent‐based models (ABMs) simulate individuals in artificial societies that are capable of movement, interaction, and transmitting disease among themselves. ABMs have been used to study the spread of disease at various spatial and temporal scales ranging from small communities to the world, over days, months, and years. The representations of space and time often vary between different epidemic ABMs and can be influenced by factors such as the size of a modeled population, computational requirements, population environments, and disease‐related data. The influence that the representations of space and time have on epidemic ABMs is difficult to assess. Here we show that the finest representations of space and time—termed spatial and temporal granularities (STGs)—in a parsimonious ABM affect speed, intensity, and spatial spread of a synthetic disease. Specifically, we found disease spread faster and more intensely as spatial granularity is coarsened, whereas disease spread slower and less intensely as temporal granularity is coarsened in a parsimonious ABM. Our study is the first to use the same epidemic ABM to examine the influence of STGs. Our results demonstrate that STGs influence ABM dynamics including early disease burnout and that an interrelationship exists between the coarsening of STGs and the speed and intensity at which disease spreads. Our parsimonious ABM is extended based on a structured community model and we found STGs also influence ABM dynamics in a more realistic context that includes hierarchical movement. Broadly, our study serves as a basis for further inquiry toward the influence of space–time representations on more realistic models that include multiscale mobility, routine movements (e.g., commuting), and heterogeneous population distributions.     

p‐Functional Clusters Location Problem for Detecting Spatial Clusters with Covering Approach

Regionalization or districting problems commonly require each individual spatial unit to participate exclusively in a single region or district. Although this assumption is appropriate for some regionalization problems, it is less realistic for delineating functional clusters, such as metropolitan areas and trade areas where a region does not necessarily have exclusive coverage with other regions. This paper develops a spatial optimization model for detecting functional spatial clusters, named the p‐functional clusters location problem (p‐FCLP), which has been developed based on the Covering Location Problem. By relaxing the complete and exhaustive assignment requirement, a functional cluster is delineated with the selective spatial units that have substantial spatial interaction. This model is demonstrated with applications for a functional regionalization problem using three journey‐to‐work flow datasets: (1) among the 46 counties in South Carolina, (2) the counties in the East North Central division of the US Census, and (3) all counties in the US. The computational efficiency of p‐FCLP is compared with other regionalization problems. The computational results show that detecting functional spatial clusters with contiguity constraints effectively solves problems with optimality in a mixed integer programming (MIP) approach, suggesting the ability to solve large instance applications of regionalization problems.     

Quantifying Animal Trajectories Using Spatial Aggregation and Sequence Analysis: A Case Study of Differentiating Trajectories of Multiple Species

The increasing availability of telemetry data with high spatial and temporal resolution promises to greatly advance scientific understandings of the movement patterns of individual organisms across space and time. The amount of data provided by such methods, however, can be challenging to analyze and interpret. In this study, we present a new approach for analyzing animal movements that aggregates telemetry locations into spatial clusters and extracts the information from sequences formed by individuals passing through these spatial clusters. We applied this integrated approach of spatial aggregation and sequence analysis to quantify and compare trajectories of cattle (Bos taurus), mule deer (Odocoileus hemionus), and elk (Cervus elaphus) tracked by automated telemetry at the Starkey Experimental Forest and Range in northeastern Oregon, USA. Our approach effectively differentiated movement patterns of the three species. It provides a useful mean of quantifying movement patterns of species in a landscape.     

旅游地复杂系统演化理论研究流派、进程与展望

以系统科学发展历程为脉络,梳理现今蓬勃发展的旅游地复杂系统演化理论研究成果,辨析了不同流派的核心概念、理论体系、研究方法,探寻该领域研究的共同纲领与范式尚未形成的内在原因,提出摒弃现有不同理论观点之差异,集各家之所长,以"非线性思维"、"整体思维"、"关系思维"及"过程思维"的系统科学探究方式为指导,以系统要素间耦合关系及其思想为进程构建旅游地复杂系统演化理论研究框架,并展望了今后的研究方向与思路。     

Exploring patterns of movement suspension in pedestrian mobility

One of the main tasks in analyzing pedestrian movement is to detect places where pedestrians stop, as those places usually are associated with specific human activities, and they can allow us to understand pedestrian movement behavior. Very few approaches have been proposed to detect the locations of stops in positioning data sets, and they often are based on selecting the location of candidate stops as well as potential spatial and temporal thresholds according to different application requirements. However, these approaches are not suitable for analyzing the slow movement of pedestrians where the inaccuracy of a nondifferential global positioning system commonly used for movement tracking is so significant that it can hinder the selection of adequate thresholds. In this article, we propose an exploratory statistical approach to detect patterns of movement suspension using a local indicator of spatial association (LISA) in a vector space representation. Two different positioning data sets are used to evaluate our approach in terms of exploring movement suspension patterns that can be related to different landscapes: players of an urban outdoor mobile game and visitors of a natural park. The results of both experiments show that patterns of movement suspension were located at places such as checkpoints in the game and different attractions and facilities in the park. Based on these results, we conclude that using LISA is a reliable approach for exploring movement suspension patterns that represent the places where the movement of pedestrians is temporally suspended by physical restrictions (e.g., checkpoints of a mobile game and the route choosing points of a park).     

The Saddlepoint Approximation of Moran's I's and Local Moran's Ii's Reference Distributions and Their Numerical Evaluation

Global Moran's I and local Moran's I_i are the most commonly used test statistics for spatial autocorrelation in univariate map patterns or in regression residuals. They belong to the general class of ratios of quadratic forms for whom a whole array of approximation techniques has been proposed in the statistical literature, such as the prominent saddlepoint approximation by Offer Lieberman (1994). The saddlepoint approximation outperforms other approximation methods with respect to its accuracy and computational costs. In addition, only the saddlepoint approximation is capable of handling, in analytical terms, reference distributions of Moran's I that are subject to significant underlying spatial processes. The accuracy and computational benefits of the saddlepoint approximation are demonstrated for a set of local Moran's Ii statistics under either the assumption of global spatial independence or subject to an underlying global spatial process. Local Moran's I_i is known to have an excessive kurtosis and thus void the use of the simple approximation methods of its reference distribution. The results demonstrate how well the saddlepoint approximation fits the reference distribution of local Moran's I_i. Furthermore, for local Moran's I_i under the assumption of global spatial independence several algebraic simplifications lead to substantial gains in numerical efficiency. This makes it possible to evaluate local Moran's I_i's significance in large spatial tessellations.     

Adaptation,interaction and urgency: a complex evolutionary economic geography approach to leisure

Local and regional governments in western European peripheral areas aim to spur leisure-led regional development. We explore planning for leisure by applying an evolutionary economic geography (EEG) approach from a complexity perspective. We identify conditions which enable and constrain leisure development and its effects on the region as a whole. This means combining the local level of individual adaptations with the institutional setting and with the regional scale. We examine the Dutch province of Fryslân and explore by means of case study analysis how current leisure development processes can be explained in a complex evolutionary manner. We explore economic novelty as a result of individual adaptations; how such adaptations through interactions create emerging spatial patterns; how these spatial patterns form self-organizing new types of order; and the way this process is dependent on previous paths whilst also creating new pathways. Our findings show that although development is dependent on individual adaptations often stemming from a few actors, for such adaptations to have an effect on the region requires a connectivity between actors and a sense of urgency amongst those actors. Using a complex EEG approach allows us to explain leisure-led regional development as the product of these conditions. This can help planners deal with the complexity and unpredictability of this process, focusing not on a desired end goal as such, but on creating the conditions in which a more autonomous development can take place.     

Elementary Spatial Systems of Industrial Production

An elementary spatial system of industrial production is conceptualized as the primary geographical formation in industry. Such an elementary production system (EPS) is viewed as consisting of raw-material and consumption nodes connected by lines of movement with a single production node. Besides the measures proposed by Kansky (University of Chicago, Research Paper 84, 1963), such a system, represented in the form of a connected, directed graph, can be described by measures of material and spatial transformation and by indices of dispersion of aggregate nodes. Characteristic properties of EPS are the spatial attraction between nodes and the spatial coincidence and intersection of common nodes of two or more systems. The usual Weberian movement-minimization approach to the building of a model of such an elementary production system is judged to be inadequate because it ignores local differences in production costs, and a “field of potential costs” is proposed instead to take account of the total cost picture.     

Adaptive Cell Tower Location Using Geostatistics. 基于地统计学的适应性基站发射塔选址研究

In this article, we address the problem of allocating an additional cell tower (or a set of towers) to an existing cellular network, maximizing the call completion probability. Our approach is derived from the adaptive spatial sampling problem using kriging, capitalizing on spatial correlation between cell phone signal strength data points and accounting for terrain morphology. Cell phone demand is reflected by population counts in the form of weights. The objective function, which is the weighted call completion probability, is highly nonlinear and complex (nondifferentiable and discontinuous). Sequential and simultaneous discrete optimization techniques are presented, and heuristics such as simulated annealing and Nelder–Mead are suggested to solve our problem. The adaptive spatial sampling problem is defined and related to the additional facility location problem. The approach is illustrated using data on cell phone call completion probability in a rural region of Erie County in western New York, and accounts for terrain variation using a line‐of‐sight approach. Finally, the computational results of sequential and simultaneous approaches are compared. Our model is also applicable to other facility location problems that aim to minimize the uncertainty associated with a customer visiting a new facility that has been added to an existing set of facilities.     

Laboratory and in situ assays of digital image analysis based protocols for biodeteriorated rock and mural paintings recording

Rock art paintings, and in general mural paintings, are one of the many elements of cultural heritage complex systems. As the different elements of a system have diverse spatial positions, spatial recording allows understanding their interactions. Thus, a useful approach to mural paintings recording is to understand it as a microcartography issue, managing each element of the system as a cartographic coverage.     

A Bi‐objective Optimization Model for Designing Safe Walking Routes for School Children

This study uses a mathematical optimization approach to design safe walking routes from school to home for children. Children are thought to be safer when walking together in groups rather than alone. Thus, we assume that the risk of walking along a given road segment in a group is smaller than that of walking the same segment alone. At the same time, the walking route between school and home for each child should not deviate substantially from the shortest route. We propose a bi‐objective model that minimizes both the total risk (particularly, the total distance walked alone) and the total walking distance for all children. We present an integer programming formulation of the proposed problem and apply this formulation to two instances based on actual road networks. We obtain Pareto optimal solutions using a mathematical programming solver and analyze the characteristics of the solutions and their potential applicability to real situations. The results show that the proposed model produces much better solutions compared with the solution where each child walks along the shortest path from school to home. In some optimal solutions, only a small deviation from the shortest path results in a dramatic reduction of the risk objective.     

Analyzing Cross-classified Data with Inherent Spatial Dependence

Despite considerable recent progress in the methods available for the log-linear analysis of categorical data arising from complex sampling schemes, only a few papers have been published that deal with the parallel phenomenon of dependence induced by spatial sampling. This paper aims to add to the general awareness of this topic and suggests some new ideas for tackling the problems raised. In the paper it is shown that the method that has been proposed for the valid selection of log-linear models given spatially dependent data and some derivative methods are somewhat conservative when compared to an approach based on a model of spatial dependence outlined in section 4. The method also serves as a data exploratory technique to enhance the use of the more robust conservative approach.     

Refining the definition of cultural levels at Karabi Tamchin: a quantitative approach to vertical intra-site spatial analysis

The visual identification of archaeological levels can be difficult when stratigraphy is complex. This study emphasizes the importance of three-dimensional intra-site spatial analysis as a means of testing the integrity of archaeological levels, including the identification of palimpsest deposits. A geographical information system (GIS) is applied to a three-dimensional spatial analysis of lithic and bone distributions from Karabi Tamchin, a Middle Palaeolithic site from the Crimea, Ukraine. K-means statistical clustering is combined with a series of data transformations to identify and interpret the vertical and horizontal spatial organization of the site. The results indicate that K-means cluster analysis, used in conjunction with GIS, provides an exceptional method of identifying discrete clusters of archaeological materials in three dimensions. Through an analysis of cluster contents within levels, it is possible to reconstruct and compare patterns of spatial organization at Karabi Tamchin, contributing to current debates regarding the cognitive complexity of Neanderthal populations.