The problem of identifying the shortest path along a road network is a fundamental problem in network analysis, ranging from route guidance in a navigation system to solving spatial allocation problems. Since this type of problem is solved so frequently, it is important to craft an approach that is as efficient as possible. Based upon past research it is generally accepted that several efficient implementations of the Dijkstra algorithm are the fastest at optimally solving the 'one-to-one' shortest path problem (Cherkassky, et al. 1996). We show that the most efficient, state-of-the-art implementations of Dijkstra can be improved by taking advantage of network properties associated with GIS-sourced data. The results of this paper, derived from tests of different algorithmic approaches on real road networks, will be extremely valuable for application developers and researchers in the GIS community.

The fluctuating two-ray (FTR) fading model provides a much better fit than other fading models for small-scale fading measurements in millimeter wave communications. In this paper, using a mixture of gamma distributions, new exact analytical expressions for the probability density and cumulative distribution functions of the FTR distribution with arbitrary fading parameters are presented. Moreover, the performance of digital communication systems over the FTR fading channel is evaluated in terms of the channel capacity and the bit error rate. The interaction between channel fading parameters and system performance is further investigated. Our newly derived results extend and complement previous knowledge of the FTR fading model. Index TermsFluctuating two-ray fading model, channel capacity, bit error rate.

Ensuring the physical layer security (PHY-security) of millimeter wave (mmWave) communications is one of the key factors for the success of 5G. Recent field measurements show that conventional fading models cannot accurately model the random fluctuations of mmWave signals. To tackle this challenge, the fluctuating two-ray (FTR) fading model has been proposed. In this correspondence, we comprehensively analyze the PHYsecurity in mmWave communications over FTR fading channels. More specifically, we derive analytical expressions for significant PHY-security metrics, such as average secrecy capacity, secrecy outage probability, and the probability of strictly positive secrecy capacity, with simple functions. The effect of channel parameters on the PHY-security has been validated by numerical results.

A combined study using LA-ICP-MS U-Pb dating, Hf isotopes, trace elements and the Ti-in-zircon geothermometer was carried out on zircons from the metamorphosed basic-ultrabasic rocks in the metamorphic basement of the Cathaysia Block, southwestern Zhejiang Province. The formation and metamorphic ages of the rocks from the metamorphic basement of the Cathaysia Block were determined based on zircon U-Pb geochronology. The age for the magmatic crystalline zircons from the protolith is about 1.85 Ga. The H Hf (t) values of the older zircons were from 7 to 3, with two-stage model Hf ages (T DM2 LC ) of about 2.9 to 3.4 Ga, indicating that the source material was derived from anatexis and recycling of the Archean crust. The newly formed metamorphic zircons yielded U-Pb ages of 260 230 Ma. The metamorphic temperature calculated using the Ti-in-zircon geothermometer ranged from 610 to 720 , consistent with the results from petrographic observations, indicating that the Cathaysia Block experienced an amphibolite facies metamorphism during the Indosinian. Results from this study provided an important timeframe for the tectonic evolution in South China and the Southeast Asia during the Late Permian and Early Triassic times.

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