The Fractal Theory of Central Place Geometry: A Diophantine Analysis of Fractal Generators for Arbitrary Löschian Numbers

We develop material to determine whether or not an arbitrary number is Löschian; the procedure embodied in the theorems achieves the desired result more swiftly than do previous solutions to this problem. The correspondence between a partition of the central place lattice and a quadratic form permits the rapid determination of the lattice coordinates of an arbitrary Löschian number and of the exact shape of a single fractal generator used to form an entire central place hierarchy associated with an arbitrary Löschian number. Central place hierarchies may be generated geometrically using a single shape applied initially to a hexagon and subsequently, scaled appropriately, to resultant polygons. Fractional dimensions of arbitrary central place hierarchies, measuring their “space-filling” characteristics, follow naturally from this general procedure.     

Löschian Spatial Competition in an Emerging Retail Industry

Löschian competition is traditionally thought to lead to a spatial equilibrium in which firms enter an industry and disperse across geographic space until each firm earns insufficient excess profit to attract net new entrants. This paper assesses the appropriateness of Löschian analysis using video (movie) rental establishments in Toronto as a case example. The video rental business, as we know it today, began to take shape around 1980 and has since seen much turnover. The paper describes the changing pattern of single‐site and chain stores between 1982 and 1999. I use logistic regression to predict the survival of existing establishments. Using survivorship as a proxy for profit, the paper draws conclusions about the extent to which temporal changes in video store location correspond to the tenets of Löschian competition. The coexistence of chain and single‐site stores suggests that there are distinct market niches and that single‐site stores have used a “swarming” strategy to compete against chains. Conclusions are drawn about how the retail sector might evolve in the future because of the locational competition between chains and single‐site stores.     

A Location-Allocation Model of Lösch's Central Place Theory: Testing on a Uniform Lattice Network

This paper develops a location-allocation model of Lösch's central place theory that maximizes the number of firms that can coexist in the market, subject to range, threshold, hierarchy, and other constraints. F.o.b. costs, economies of scale, and elastic demand are included. Consumer behavior postulates concerning the “nearest center hypothesis” and the “indifference principle” are formulated as nonlinear constraints but not used during solution. Methods are developed for simulating the continuous, infinite plain with a discrete, bounded network by use of an outer overflow network and a symmetrical market area constraint. The model is tested by applying it to a uniform lattice network and comparing the results to the expected pattern of nested hexagons. Solutions consistent with the k = 3, 4, and 7 patterns are generated by changing threshold values. However, remaining inconsistencies appear to be due to the inability to express the consumer behavior laws as linear constraints, to the bounded and discrete nature of the network, and to the objective function being the sum of integer variables. The long-run purpose of developing and validating a location-allocation model of a location theory is to use it to relax the theory's restrictive assumptions and to apply the theory to nonuniform regions.     

The Lösch System of Market Areas: Derivation and Extension

Certain aspects of Lösch's classic work on the network of markets and the system of networks have not yet been clearly explained in the literature. Lösch did not describe his derivation procedures in full, and apparent printing errors in certain förmulae confuse the issue further, with the result that several recent texts reproduce Lösch's diagrams but offer no explanation of how they are constructed. Accepting the network of hexagonal market areas for a continuous system of markets, given an even but discrete distribution of population, the derivation from first principles of the complete system of different market areas is presented. Apparent errors in the translated text of Lösch's work are corrected. Limitations in some other authors' work and accordance with earlier empirically derived formulae are mentioned. The production of “city-rich” and “city-poor” sectors is shown to be a constraint on, rather than a result of, the system, and Lösch's statement that the coincidence of centers is maximized is clarified. The extension of the Lösch system to the internal tertiary structure of the city is presented and attention drawn to the empirical attractiveness of this approach.     

The "Return of the Subject" As a Historico-Intellectual Problem

Recently, a call for the “return of the subject” has gained increasing influence. The power of this call is intimately linked to the assumption that there is a necessary connection between “the subject” and politics (and ultimately, history). Without a subject, it is alleged, there can be no agency, and therefore no emancipatory projects—and, thus, no history. This paper discusses the precise epistemological foundations for this claim. It shows that the idea of a necessary link between “the subject” and agency, and therefore between the subject and politics (and history) is only one among many different ones that appeared in the course of the four centuries that modernity spans. It has precise historico‐intellectual premises, ones that cannot be traced back in time before the end of the nineteenth century. Failing to observe the historicity of the notion of the subject, and projecting it as a kind of universal category, results, as we shall see, in serious incongruence and anachronisms. The essay outlines a definite view of intellectual history aimed at recovering the radically contingent nature of conceptual formations, which, it alleges, is the still‐valid core of Foucault's archeological project. Regardless of the inconsistencies in his own archeological endeavors, his archeological approach intended to establish in intellectual history a principle of temporal irreversibility immanent in it. Following his lead, the essay attempts to discern the different meanings the category of the subject has historically acquired, referring them back to the broader epistemic reconfigurations that have occurred in Western thought. This reveals a richness of meanings in this category that are obliterated under the general label of the “modern subject”; at the same time, it illuminates some of the methodological problems that mar current debates on the topic.     

The p‐Compact‐regions Problem

The p‐compact‐regions problem involves the search for an aggregation of n atomic spatial units into p‐compact, contiguous regions. This article reports our efforts in designing a heuristic framework—MERGE (memory‐based randomized greedy and edge reassignment)—to solve this problem through phases of dealing, randomized greedy, and edge reassignment. This MERGE heuristic is able to memorize (ME of MERGE) the potential best moves toward an optimal solution at each phase of the procedure such that the search efficiency can be greatly improved. A dealing phase grows seeded regions into a viable size. A randomized greedy (RG of MERGE) approach completes the regions' growth and generates a feasible set of p‐regions. The edge‐reassigning local search (E of MERGE) fine‐tunes the results toward better objectives. In addition, a normalized moment of inertia (NMI) is introduced as the method of choice in computing the compactness of each region. We discuss in detail how MERGE works and how this new compactness measure can be seamlessly integrated into different phases of the proposed regionalization procedure. The performance of MERGE is evaluated through the use of both a small and a large p‐compact‐regions problem motivated by modeling the regional economy of Southern California. We expect this work to contribute to the regionalization theory and practice literature. Theoretically, we formulate a new model for the family of p‐compact‐regions problems. The novel NMI introduced in the model provides an accurate, robust, and efficient measure of compactness, which is a key objective for p‐compact‐regions problems. Practically, we developed the MERGE heuristic, proven to be effective and efficient in solving this nonlinear optimization problem to near optimality. El problema de regiones compactas tipo p (p‐compact regions) consiste en la búsqueda de la agregación de n unidades espaciales atómicas que produzca regiones contiguas de tipo p‐compacto. Este artículo reporta los esfuerzos de los autores en el diseño de un marco heurístico MERGE (memory‐based randomized greedy and edge‐reassignment) el cual resuelve este problema a través de las fases de la negociación (dealing), codicia aleatorizada (randomized greedy), y la reasignación de bordes (edge reassignment). El heurístico MERGE es capaz de memorizar ( ME de MERGE) los mejo)res desplazamientos posibles hacia una solución óptima en cada fase del procedimiento de tal manera que la eficiencia de la búsqueda puede ser mejorada en gran medida. La fase de negociación crea regiones “sembradas” aleatoriamente y las hace crecer en diferentes tamaños . El componente de codicia aleatorio (RG de MERGE) completa la fase de crecimiento de las regiones y genera un conjunto factible de regiones tipo p. La reasignación de bordes se realiza vía una búsqueda local (E de MERGE) que afina los resultados con el fin the alcanzar los objetivos. Además, el enfoque propuesto aquí utiliza el momento de inercia normalizado (normalized momento of inertia‐NMI) como método para el cálculo de la compacidad de cada región. El artículo discute en detalle el funcionamiento de MERGE y cómo esta nueva medida compacidad puede integrarse perfectamente en las diferentes fases del procedimiento de regionalización propuesto. Para ilustrar y evaluar el desempeño de MERGE, el metodo es aplicado a dos problemas de p‐compact regions, uno grande y uno pequeño, basados en el modelado de la economía regional del sur de California. Los autores esperan que este trabajo contribuya a la literatura teórica y práctica de la regionalización. En términos teóricos, se formula un nuevo modelo de la familia de problemas de p‐compact regions. El NMI equipa al modelo con una novedosa forma de obtener una medida exacta, robusta y eficiente de compacidad, que es un objetivo clave para los problemas región compacta tipo p. En términos prácticos, se desarrolla MERGE, un procedimiento heurístico que ha demostrado ser eficaz y eficiente en la solución de este problema de optimización no lineal de manera casi óptima. p紧凑区域问题包含寻找一种聚集方法,将n个不可分割的空间单元集合成p紧凑的邻近区域。本文阐述了一种启发式架构MERGE(基于记忆的随机贪婪和边界再赋值算法),通过处理、随机贪婪和边界再分配这几个阶段解决p紧凑问题。MERGE启发式框架能存储 处理过程每个阶段中,向一个最优解的潜在最佳移动方式,从而可极大地提升搜索效率。一个处理阶段可将种子区域生长到可行大小。而一个随机贪婪阶段能完成区域增长并生成p区域的可行集。在边界再分配的局部搜索阶段对结果进行微调以达到更好的目标。此外,引入标准化的惯性矩作为每个区域紧凑度计算的选择方法。本文详细讨论了MERGE的工作原理,以及这种新的紧凑度测算方法如何能无缝地整合到所提出的区域化流程的不同阶段。通过在南部加州区域经济建模中一小一大两个p紧凑区域问题的应用,对MERGE的性能进行评估,期望该工作能够对区域化理论和实践作出贡献。理论上,提出了可解决p紧凑区域这类问题的新模型。在模型中引入新颖的标准化惯性矩这一精确的、鲁棒的和有效的紧凑度度量方法,是解决p紧凑区域问题的关键目标;实践上,本文发展了MERGE启发式框架,并证明了它在解决这种非线性优化问题近优性的有效性和高效性。     

The Misuse of Area in Mapping Census-Type Numbers

Abstract

Polish lands in 19th century are usually located in the economic peripheries of Europe. However there are no usable datasets of Polish GDP for this period to verify this hypothesis. The main problem is lack of reliable and comparable macroeconomic data from country divided between Russia, Austria and Prussia. The main goal of this research was to propose the method based on the urbanization data set to estimate the GDP of Polish territories and to verify the hypothesis on the peripheral development of Polish lands. In result the new estimates on GDP per capita were established, that allowed to confirm the hypothesis of semi-peripheral development of Polish territories in 19th century and slow process of catching-up with the core economies.     

欧洲整体的历史与整体的阐述——评《欧洲的分与合》

《欧洲的分与合》这部著作具有重大的学术价值：这是中国史学界第一次真正把欧洲作为一个整体来阐述它的历史发展,论证了当代欧洲发生巨变的必然性;标志着中国史学界在欧洲史研究领域取得了突破性进展。《欧洲的分与合》以其对欧洲整体的历史作出整体阐述的风格,超越了以往众多的欧洲史著作。     

The Price Theory of Thünen's Theory of Rent: Assumptions and Implications of a Familiar Model

Economic forces in the Thünen rent diagram and the equivalence of certain Thünian and Ricardian land rent concepts are shown diagrammatically. The usual, linear rent line requires fixed production coefficients in agriculture and constant costs in transportation. The ability to substitute among land and other inputs in agriculture makes the rent line convex to the origin, as do decreasing costs in transportation. Increasing cost transportation makes the rent line concave. Traditional, subsistence agriculture is likely to produce a more strongly convex rent line than modern, large-scale agriculture.
Les forces économiques dans le diagramme de rente de Thünen et l'equivalence de certains concepts de rente foncier Thünien et Ricardien sont exposés graphiquement. La courbe de rente linéaire exige des coëfficients de production fixes en agriculture et des coûts de transport fixes. La capacitéà substituer entre la terre et d'autres facteurs de production en agriculture, ainsi que des coûts de transport décroissants, donnent une courbe de rente convexe par rapport à 1'origine. Des coûts de transport accroissants donnent une courbe de rente concave. Une agriculture à petite échelle, traditionnelle, donnera probablement une courbe de rente plus convexe qu'une agriculture moderne, à grande échelle.