Publisher's Note: Generic patterns in the evolution of urban water networks: Evidence from a large Asian city [Phys. Rev. E 95 , 032312 (2017)]

Abstract

This paper was published online on 9 March 2017 with an error in Eq. (1b) and surrounding text and in the caption to Fig. 6. The caption of Fig. 6 should read as "WDN subnets along a gradient of breaking points between the power laws of trunk and tail (k break outliers from panel (d) in Fig. 5): (a) DZ11: k break = 5, p(k) trunk = 0.40k −2.49 and p(k) tail = 0.09 k −1.47 , N = 2425 (dual-mapped nodes); (b) DZ10: k break = 8, p(k) trunk = 1.46k −2.80 and p(k) tail = 0.26k −1.88 , N = 3179; (c) DZ01: k break = 10, p(k) trunk = 1.17k −2.37 and p(k) tail = 0.138k −1.686 , N = 1497; (d) DZ32: in this subnet power-law distributions of trunk and tail converge as the breaking point between the two power laws increases (k break = 20), and p(k) = 1.07k −2.27 (N = 2271)." On page 2, left-hand column, the text above Eqs. (1a) and (1b) should read as "The node degree distributions (NDD) for both types of water networks can be approximated by a Pareto power-law distribution [Eq. (1a); large, mature networks], p(k) = ak −γ , (1a) for k 2, or a double Pareto power-law distribution [Eq. (1b); small, immature networks], described by a two-piece function in the form p(k) trunk = ak −γ trunk , p(k) tail = bk −γ tail , (1b) where k 2 for p(k) trunk and k k break for p(k) tail. The exponent, γ [Eq. (1a)] and γ trunk [Eq. (1b)], for both WDNs and SSNs converges above a threshold of network size, measured as dual-mapped nodes N > 10 2 ." The paper has been corrected as of 25 February 2019. The caption and text are incorrect in the printed version of the journal.

Dynamics of functional failures and recovery in complex road networks

“…The concept of dual representation is different from the "dual graph" in graph theory, which relates to the faces of planar graphs. The Hierarchical Intersection Continuity Negotiation (HICN) model [25,26] is among the best dual representation approaches for road networks. According to HICN, two consecutive road segments belong to the same road if they have same road class and the convex angle they form is close to 180 degree.…”

Uncovering the Fractal Nature of Water Vapor Distribution above the Surface of the Earth

“…Numerous attempts [8][9][10][11][12][13][14][15][16][17][18][19] that elucidate the spatio-temporal patterns of land surface temperature (LST) and reveal the scaling properties in these distributions motivated us to study the fractal analysis of the distribution of water vapour data. Based on theory, fractal analysis can be used to decompose irregular data sets to many microscopic pictures on multiple scales and reveal their scaling properties in various geospatial distributions.…”

“…Accurate quantification of water vapour data and the interpretation of its physical characteristics are crucial in understanding how global climate systems, such as global warming, are changing over time. Urban land use [20,21], urban infrastructure [22], and network distributions [23][24][25] have been studied using fractal based analyses and techniques. Similar techniques have also been developed for atmospheric sciences [26].…”