Origin of power laws and their spatial fractal structure for city-size distributions

City-size distributions follow an approximate power law in various countries despite high volatility in relative city sizes over time. Our empirical evidence for the United States indicates that the scaling law stems from a spatial fractal structure owing to the coordination of industrial locations. While the locations of individual industries change considerably over time, there is a persistent pattern in that the localized industries at a given time are found only in larger cities. The spatial organization of cities exhibits a stable hierarchical structure in which larger cities are spaced apart to serve as centers for surrounding smaller cities, generating a recursive pattern across different spatial scales. In our theoretical replication of the observed regularities, diversity in scale economy among industries induces diversity in their location pattern, which translates into diversity in city size via spatial coordination of industries and population. The city-size power law is a generic feature of Monte-Carlo samples of stationary states resulting from the spontaneous spatial fractal structure in the hypothetical economy. The identified regularities reveal constraints on feasible urban planning at each regional scale. The success or failure of place-based policies designed to take advantage of individual cities' characteristics should depend on their spatial relationships with other cities, subject to the nationwide spatial fractal structure

Differential determinants of physical daily activities in frail and nonfrail community-dwelling older adults

AbstractBackground/PurposeThe purpose of this study was to determine whether or not daily activities determined by average daily steps are associated with age, gender, body mass index, fear of falling, and physical functions (locomotive function, balance function, and muscle power) in community-dwelling nonfrail and frail older adults.MethodsThis is a cross-sectional study conducted in community-dwelling older adults in Japan. Based on the Timed Up and Go (TUG) test, 629 elderly adults were divided into two groups: 515 were grouped to nonfrail elderly (TUG time less than 13.5 seconds, mean age 77.0±7.2 years) and 114 to frail elderly (TUG time of 13.5 seconds or more, mean age 76.1±7.5 years). Daily physical activities were determined by average daily steps measured by pedometer and four other physical function tests (10-m walk test, single-leg standing, functional reach, and five-chair stand test) were performed along with the assessment of fear of falling.ResultsStepwise regression analysis revealed that age, gender, 10-m walk test, and single-leg standing were significant and independent determinants of the average step counts in the nonfrail elderly (R2=0.282, p<0.001), whereas fear of falling was the only significant and independent determinant of the average step counts in the frail elderly (R2=0.119, p<0.001).ConclusionThese results indicate that differential factors may be related to daily activities depending on the level of frailty in community-dwelling older adults

Ambipolar Organic Field-Effect Transistors Based on Indigo Derivatives

In order to improve the ambipolar performance of indigo-based semiconductors, we have investigated halogen-substituted (1 - 4) and phenyl-substituted (5) indigo derivatives at the 5-position. We show that introduction of iodine atoms, namely 5,5'-diiodoindigo (4), leads to the strong halogen-halogen interaction (iodine-iodine interaction) that gives a significant effect on the molecular packing. Thanks to the supramolecular network coming from the extra iodine-iodine interaction, the molecules are arranged approximately perpendicular to the substrate in the thin film. This results in remarkable transistor performance of the maximum hole and electron mobilities (µh/µe) = 0.42/0.85 cm2V–1s–1, which are one of the highest among small-molecule ambipolar organic transistors. Furthermore, introducing phenyl groups, 5 improves the transistor performances up to the maximum mobilities µh/µe = 0.56/0.95 cm2V–1s–1. We have found that the phenyl groups destroy the standard molecular packing of indigo to achieve a unique structure that is a hybrid of the herringbone and brickwork structures

Endogenous agglomeration in a many-region world

We study a general family of economic geography models that features endogenous agglomeration. In many-region settings, the spatial scale---"global" or "local"---of the dispersion force(s) in a model plays a key role in determining the resulting endogenous spatial patterns and comparative statics. A global dispersion force accrues from competition between different locations and leads to the formation of multiple economic clusters (or cities). A local dispersion force is caused by crowding effects within each location and induces the flattening of each city. By distinguishing local and global dispersion forces, we can define three prototypical classes, namely, models that have only global, only local, and both local and global dispersion forces. The three model classes engender qualitatively different spatial patterns. Multiple cities are formed only when a global dispersion force is at work; otherwise, only a unimodal distribution can be formed. A city can have its spatial extent only when a local dispersion force is at work. A wide variety of extant models are reduced into the three prototypical classes. Our framework adds consistent interpretations to the empirical literature and also provides general \Red{insights into} treatment effects in structural economic geography models.Comment: Main text: 53 pages, 18 figure