Metric and topo-geometric properties of urban street networks: some convergences, divergences, and new results

The theory of cities, which has grown out of the use of space syntax techniques in urban studies, proposes a curious mathematical duality: that urban space is locally metric but globally topo-geometric. Evidence for local metricity comes from such generic phenomena as grid intensification to reduce mean trip lengths in live centres, the fall of movement from attractors with metric distance, and the commonly observed decay of shopping with metric distance from an intersection. Evidence for global topo-geometry come from the fact that we need to utilise both the geometry and connectedness of the larger scale space network to arrive at configurational measures which optimally approximate movement patterns in the urban network. It might be conjectured that there is some threshold above which human being use some geometrical and topological representation of the urban grid rather than the sense of bodily distance to making movement decisions, but this is unknown. The discarding of metric properties in the large scale urban grid has, however, been controversial. Here we cast a new light on this duality. We show first some phenomena in which metric and topo-geometric measures of urban space converge and diverge, and in doing so clarify the relation between the metric and topo-geometric properties of urban spatial networks. We then show how metric measures can be used to create a new urban phenomenon: the partitioning of the background network of urban space into a network of semi-discrete patches by applying metric universal distance measures at different metric radii, suggesting a natural spatial area-isation of the city at all scales. On this basis we suggest a key clarification of the generic structure of cities: that metric universal distance captures exactly the formally and functionally local patchwork properties of the network, most notably the spatial differentiation of areas, while the top-geometric measures identifying the structure which overcomes locality and links the urban patchwork into a whole at different scales

Metric and topo-geometric properties of urban street networks: some convergences, divergences and new results

The theory of cities, which has grown out of the use of space syntax techniques in urban studies, proposes a curious mathematical duality: that urban space is locally metric but globally topo-geometric. Evidence for local metricity comes from such generic phenomena as grid intensification to reduce mean trip lengths in live centres, the fall of movement from attractors with metric distance, and the commonly observed decay of shopping with metric distance from an intersection. Evidence for global topo-geometry come from the fact that we need to utilise both the geometry and connectedness of the larger scale space network to arrive at configurational measures which optimally approximate movement patterns in the urban network. It might be conjectured that there is some threshold above which human being use some geometrical and topological representation of the urban grid rather than the sense of bodily distance to making movement decisions, but this is unknown. The discarding of metric properties in the large scale urban grid has, however, been controversial. Here we cast a new light on this duality. We show first some phenomena in which metric and topo-geometric measures of urban space converge and diverge, and in doing so clarify the relation between the metric and topo-geometric properties of urban spatial networks. We then show how metric measures can be used to create a new urban phenomenon: the partitioning of the background network of urban space into a network of semi-discrete patches by applying metric universal distance measures at different metric radii, suggesting a natural spatial area-isation of the city at all scales. On this basis we suggest a key clarification of the generic structure of cities: that metric universal distance captures exactly the formally and functionally local patchwork properties of the network, most notably the spatial differentiation of areas, while the top-geometric measures identifying the structure which overcomes locality and links the urban patchwork into a whole at different scales

Transient Relativistically-Shifted Lines as a Probe of Black Hole Systems

X-ray spectra of Seyfert galaxies have revealed a new type of X-ray spectral feature, one which appears to offer important new insight into the black hole system. XMM/Chandra revealed several narrow emission lines redward of Fe Kalpha in NGC 3516. Since that discovery the phenomenon has been observed in other Seyfert galaxies, e.g. NGC 7314 and ESO 198-G24. We present new evidence for a redshifted Fe line in XMM spectra of Mrk 766. These data reveal the first evidence for a significant shift in the energy of such a line, occurring over a few tens of kiloseconds. This shift may be interpreted as deceleration of an ejected blob of gas traveling close to the escape velocity.Comment: 13 pages, 5 figures (4 color) accepted by Ap

Rehabilitation interventions for foot drop in neuromuscular disease

"Foot drop" or "Floppy foot drop" is the term commonly used to describe weakness or contracture of the muscles around the ankle joint. It may arise from many neuromuscular diseases

The Variable X-ray Spectrum of Markarian 766 - II. Time-Resolved Spectroscopy

CONTEXT: The variable X-ray spectra of AGN systematically show steep power-law high states and hard-spectrum low states. The hard low state has previously been found to be a component with only weak variability. The origin of this component and the relative importance of effects such as absorption and relativistic blurring are currently not clear. AIMS: In a follow-up of previous principal components analysis, we aim to determine the relative importance of scattering and absorption effects on the time-varying X-ray spectrum of the narrow-line Seyfert 1 galaxy Mrk~766. METHODS: Time-resolved spectroscopy, slicing XMM and Suzaku data down to 25 ks elements, is used to investigate whether absorption or scattering components dominate the spectral variations in Mrk 766.Time-resolved spectroscopy confirms that spectral variability in Mrk 766 can be explained by either of two interpretations of principal components analysis. Detailed investigation confirm rapid changes in the relative strengths of scattered and direct emission or rapid changes in absorber covering fraction provide good explanations of most of the spectral variability. However, a strong correlation between the 6.97 keV absorption line and the primary continuum together with rapid opacity changes show that variations in a complex and multi-layered absorber, most likely a disk wind, are the dominant source of spectral variability in Mrk 76

Structure of deformed silicon and implications for low cost solar cells

The microstructure and minority carrier lifetime of silicon were investigated in uniaxially compressed silicon samples. The objective of the investigation was to determine if it is feasible to produce silicon solar cells from sheet formed by high temperature rolling. The initial structure of the silicon samples ranged from single crystal to fine-grained polycrystals. The samples had been deformed at strain rates of 0.1 to 8.5/sec and temperatures of 1270-1380 C with subsequent annealing at 1270-1380 C. The results suggest that high temperature rolling of silicon to produce sheet for cells of high efficiency is not practical

Direct Measurement of the X-ray Time-Delay Transfer Function in Active Galactic Nuclei

The origin of the observed time lags, in nearby active galactic nuclei (AGN), between hard and soft X-ray photons is investigated using new XMM-Newton data for the narrow-line Seyfert I galaxy Ark 564 and existing data for 1H0707-495 and NGC 4051. These AGN have highly variable X-ray light curves that contain frequent, high peaks of emission. The averaged light curve of the peaks is directly measured from the time series, and it is shown that (i) peaks occur at the same time, within the measurement uncertainties, at all X-ray energies, and (ii) there exists a substantial tail of excess emission at hard X-ray energies, which is delayed with respect to the time of the main peak, and is particularly prominent in Ark 564. Observation (i) rules out that the observed lags are caused by Comptonization time delays and disfavors a simple model of propagating fluctuations on the accretion disk. Observation (ii) is consistent with time lags caused by Compton-scattering reverberation from material a few thousand light-seconds from the primary X-ray source. The power spectral density and the frequency-dependent phase lags of the peak light curves are consistent with those of the full time series. There is evidence for non-stationarity in the Ark 564 time series in both the Fourier and peaks analyses. A sharp `negative' lag (variations at hard photon energies lead soft photon energies) observed in Ark 564 appears to be generated by the shape of the hard-band transfer function and does not arise from soft-band reflection of X-rays. These results reinforce the evidence for the existence of X-ray reverberation in type I AGN, which requires that these AGN are significantly affected by scattering from circumnuclear material a few tens or hundreds of gravitational radii in extent.Comment: Accepted for publication in Ap