A Fractal Perspective on Scale in Geography

Scale is a fundamental concept that has attracted persistent attention in geography literature over the past several decades. However, it creates enormous confusion and frustration, particularly in the context of geographic information science, because of scale-related issues such as image resolution, and the modifiable areal unit problem (MAUP). This paper argues that the confusion and frustration mainly arise from Euclidean geometric thinking, with which locations, directions, and sizes are considered absolute, and it is time to reverse this conventional thinking. Hence, we review fractal geometry, together with its underlying way of thinking, and compare it to Euclidean geometry. Under the paradigm of Euclidean geometry, everything is measurable, no matter how big or small. However, geographic features, due to their fractal nature, are essentially unmeasurable or their sizes depend on scale. For example, the length of a coastline, the area of a lake, and the slope of a topographic surface are all scale-dependent. Seen from the perspective of fractal geometry, many scale issues, such as the MAUP, are inevitable. They appear unsolvable, but can be dealt with. To effectively deal with scale-related issues, we introduce topological and scaling analyses based on street-related concepts such as natural streets, street blocks, and natural cities. We further contend that spatial heterogeneity, or the fractal nature of geographic features, is the first and foremost effect of two spatial properties, because it is general and universal across all scales. Keywords: Scaling, spatial heterogeneity, conundrum of length, MAUP, topological analysisComment: 12 pages, 5 figures, and one tabl

Density-matrix renormalisation group approach to quantum impurity problems

A dynamic density-matrix renormalisation group approach to the spectral properties of quantum impurity problems is presented. The method is demonstrated on the spectral density of the flat-band symmetric single-impurity Anderson model. We show that this approach provides the impurity spectral density for all frequencies and coupling strengths. In particular, Hubbard satellites at high energy can be obtained with a good resolution. The main difficulties are the necessary discretisation of the host band hybridised with the impurity and the resolution of sharp spectral features such as the Abrikosov-Suhl resonance.Comment: 16 pages, 6 figures, submitted to Journal of Physics: Condensed Matte

Some strategic national initiatives for the Swedish education in the geodata field

Ponencias, comunicaciones y pósters presentados en el 17th AGILE Conference on Geographic Information Science "Connecting a Digital Europe through Location and Place", celebrado en la Universitat Jaume I del 3 al 6 de junio de 2014.This paper describes national cooperation in Sweden launched by its universities and authorities, aimed at improving geodata education. These initiatives have been focused upon providing common access to geodata, the production of teaching materials in Swedish and organizing annual meetings for teachers. We argue that this type of cooperation is vital to providing high quality education for a poorly recognized subject in a country with a relatively small population

Supercooling of the disordered vortex lattice in Bi_2Sr_2CaCu_2O_8+d

Time-resolved local induction measurements near to the vortex lattice order-disorder transition in optimally doped Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ single crystals shows that the high-field, disordered phase can be quenched to fields as low as half the transition field. Over an important range of fields, the electrodynamical behavior of the vortex system is governed by the co-existence of the two phases in the sample. We interpret the results in terms of supercooling of the high-field phase and the possible first order nature of the order-disorder transition at the ``second peak''.Comment: 4 pages, 3 figures. Submitted to Nature, July 10th, 1999; Rejected August 8th for lack of broad interest Submitted to Physical Review Letters September 10th, 199

Long XMM observation of the Narrow-Line Seyfert 1 galaxy IRAS13224-3809: rapid variability, high spin and a soft lag

Results are presented from a 500ks long XMM-Newton observation of the Narrow-Line Seyfert 1 galaxy IRAS13224-3809. The source is rapidly variable on timescales down to a few 100s. The spectrum shows strong broad Fe-K and L emission features which are interpreted as arising from reflection from the inner parts of an accretion disc around a rapidly spinning black hole. Assuming a power-law emissivity for the reflected flux and that the innermost radius corresponds to the innermost stable circular orbit, the black hole spin is measured to be 0.988 with a statistical precision better than one per cent. Systematic uncertainties are discussed. A soft X-ray lag of 100s confirms this scenario. The bulk of the power-law continuum source is located at a radius of 2-3 gravitational radii.Comment: 7 pages, 14 figures, submitted to MNRA

Obesity and Low-Grade Inflammation Increase Plasma Follistatin-Like 3 in Humans

Background. Rodent models suggest that follistatin-like 3 (fstl3) is associated with diabetes and obesity. In humans, plasma fstl3 is reduced with gestational diabetes. In vitro, TNF-induces fstl3 secretion, which suggests a link to inflammation. Objective. To elucidate the association between plasma fstl3 and obesity, insulin resistance, and low-grade inflammation in humans. Study Design. Plasma fstl3 levels were determined in a cross-sectional study including three groups: patients with type 2 diabetes, impaired glucose tolerance, and healthy controls. In addition, lipopolysaccharide (LPS), TNF-, or interleukin-6 (IL-6) as well as a hyperinsulinemic euglycemic clamp were used to examine if plasma fstl3 was acutely regulated in humans. Results. Plasma fstl3 was increased in obese subjects independent of glycemic state. Moreover, plasma fstl3 was positively correlated with fat mass, plasma leptin, fasting insulin, and HOMA B and negatively with HOMA S. Furthermore plasma fstl3 correlated positively with plasma TNF-and IL-6 levels. Infusion of LPS and TNF-, but not IL-6 and insulin, increased plasma fstl3 in humans. Conclusion. Plasma fstl3 is increased in obese subjects and associated with fat mass and low-grade inflammation. Furthermore, TNF-increased plasma fstl3, suggesting that TNF-is one of the inflammatory drivers of increased systemic levels of fstl3

A highly-ionized absorber in the X-ray binary 4U 1323-62: a new explanation for the dipping phenomenon

We report the detection of narrow Fe XXV and Fe XXVI X-ray absorption lines at 6.68 +/- 0.04 keV and 6.97 +/- 0.05 keV in the persistent emission of the dipping low-mass X-ray binary 4U 1323-62 during a 2003 January XMM-Newton observation. These features are superposed on a broad emission feature centered on 6.6 {+0.1}{-0.2} keV. During dipping intervals the equivalent width of the Fe XXV feature increases while that of the Fe XXVI feature decreases, consistent with the presence of less strongly ionized material in the line-of-sight. As observed previously, the changes in the 1.0-10 keV spectrum during dips are inconsistent with a simple increase in absorption by cool material. However, the changes in both the absorption features and the continuum can be modeled by variations in the properties of an ionized absorber. No partial covering of any component of the spectrum, and hence no extended corona, are required. From persistent to deep dipping the photo-ionization parameter, Xi, expressed in erg cm s^{-1}, decreases from log(Xi) of 3.9 +/- 0.1 to log(Xi) of 3.13 +/- 0.07, while the equivalent hydrogen column density of the ionized absorber increases from (3.8 +/- 0.4) 10^{22} atoms cm^{-2} to (37 +/- 2) 10^{22} atoms cm^{-2}. Since highly-ionized absorption features are seen from many other dip sources, this mechanism may also explain the overall changes in X-ray spectrum observed during dipping intervals from these systems.Comment: 16 pages, major improvements following referee's report, most figures and tables changed, one figure added, accepted for publication by Astronomy and Astrophysic

The X-ray luminous cluster underlying the bright radio-quiet quasar H1821+643

We present a Chandra observation of the only low redshift, z=0.299, galaxy cluster to contain a highly luminous radio-quiet quasar, H1821+643. By simulating the quasar PSF, we subtract the quasar contribution from the cluster core and determine the physical properties of the cluster gas down to 3 arcsec (15 kpc) from the point source. The temperature of the cluster gas decreases from 9.0\pm0.5 keV down to 1.3\pm0.2 keV in the centre, with a short central radiative cooling time of 1.0\pm0.1 Gyr, typical of a strong cool-core cluster. The X-ray morphology in the central 100 kpc shows extended spurs of emission from the core, a small radio cavity and a weak shock or cold front forming a semi-circular edge at 15 arcsec radius. The quasar bolometric luminosity was estimated to be 2 x 10^{47} erg per sec, requiring a mass accretion rate of 40 Msolar per yr, which corresponds to half the Eddington accretion rate. We explore possible accretion mechanisms for this object and determine that Bondi accretion, when boosted by Compton cooling of the accretion material, could provide a significant source of the fuel for this outburst. We consider H1821+643 in the context of a unified AGN accretion model and, by comparing H1821+643 with a sample of galaxy clusters, we show that the quasar has not significantly affected the large-scale cluster gas properties.Comment: 20 pages, 19 figures, accepted by MNRA