Massive bike-sharing systems (BSS) usage and performance data have been collected for years over various locations. Nevertheless, researchers encountered several challenges while dealing with massive BSS data. The challenges that could be enhanced in the previous studies are 1) reducing high dimensionality and noise of BSS time series data and 2) extracting informative usage patterns out of massive BSS data. This paper extracts patterns and reduce data dimensions of BSS usage by exploring time series representation and clustering of BSS usage data. A reduced dimension allows us to efficiently approximate the BSS usage with reasonable accuracy, which can be further used for bike usage clustering, classification and prediction. We employ a non-data adaptive representation technique-Discrete Wavelet Transform (DWT) to reduce dimensionality and filter out random errors of the raw time series. Time series are clustered using k-means based on similarities measured by Dynamic Time Warping (DTW) and prototypes computed using DTW barycenter averaging (DBA). The proposed approaches are applied on a 3-month bike usage dataset acquired on the BSS of Chicago. The analysis results show that DWT can effectively reduce dimensionality, filter out random errors and reveal the main characteristics of the raw time series. The clustering approach offers the ability to differentiate and discover bike usage patterns across different stations. INDEX TERMS Sharing bike system, time series data mining, dynamic time warping (DWT), DTW barycenter averaging (DBA).

In order to study the effect of cement-sand ratio on the dynamic mechanical properties of the full tailings cemented backfilling, three sets of full tailings cemented backfilling specimens with different cement-sand ratios were prefabricated. The uniaxial impact of the prefabricated specimens was performed by the Ф50 mm SHPB test system. Test results showed that full tailings cemented backfilling had strong reflection and damping effects on elastic wave propagation. At lower strain rates, specimens presented strength hardening, and at higher strain rates, the test specimens presented rapid-softening strength; the strength-hardened specimen reached the peak stress at 40 μs, and the softening specimen reached the peak stress at about 18 μs; with the increase of strain rate, dynamic compressive strength, growth factor of dynamic strength, peak strain, and dynamic-static strain ratio of specimens increased totally. When the cement-sand ratio increased, ultimate dynamic compressive strength, limit dynamic strength growth factor, and ultimate peak strain of the specimen were higher; at the same strain rate, with the increase of cement content, the dynamic compressive strength, dynamic strength growth factor, and dynamic-static strain ratio of the test piece all decreased. The failure mode of the specimen was crushing failure. Under the same strain rate, when the cement content decreased, there was a higher damage degree of specimens.

Most existing bike usage prediction studies aim at building models to fit continuous bike usage data rather than categorical data, which may result in an over-fitting problem and therefore reduce the potential of the model to capture more generalized trends in bike usage predictions. This study explores a multi-categorical probabilistic approach for sharing bike demand prediction. In order to overcome the weakness of using single point measurements to describe bike usage conditions, we prepare three alternatives to capture the range, local variation, and trend of bike usage over a short-time period. The suitable indicator variables are determined based on the Principal Component Analysis (PCA) results. The Gaussian Mixture Models (GMM) is adopted to cluster homogeneous bike usage states. Then, a Markov chain model is developed based on the identified states to forecast the categorical changes of bike usage. Finally, to examine the effectiveness of the proposed approach, the persistence model is employed as a benchmark and two measures-Percent Correct (PC) and Heidke Skill Score (HSS), are introduced to quantify categorical data prediction performance. The results show that the proposed approach is able to offer high accuracy, skill, reliability, and discrimination at suitable prediction intervals.INDEX TERMS Gaussian mixture models, Markov chain model, sharing bike, multi-categorical forecast.

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The rumor-free equilibrium state and rumor-endemic equilibrium state are two symmetric descriptions of the status of a system. The constant spreading of rumors would affect the smooth operation of emergency management procedures and cause unnecessary social and economic loss. To reduce the negative effect of rumor propagation, in this paper, we introduce a compartmental model of rumor propagation, which considers the rumor refutation of public and information feedback. By deriving mean-field equations that describe the dynamics of the model, we use analytical and numerical solutions of these equations to investigate the threshold and dynamics of the model in both the closed system and open system. The results imply that the initial equilibrium point is not stable and there exists a rumor-free equilibrium point; in the open system, there exists a threshold beyond which rumors can spread; the stability of the initial equilibrium point is related to the threshold R0 = (φ*α)/μ, and there exists a rumor-endemic equilibrium point. The development process of rumor propagation can be divided into four stages: latent period, progressive period, intense period, and recession period. Under the influence of population, rumor spreading can exceed the threshold readily because the migration rate μ is usually less than the proportion of ignorants without critical ability φ, and the rumor spreading process in an open system presents a fluctuating development, the rumor would not disappear in this autonomous system. Based on the analysis, we propose some measures, such as providing open and efficient information queries and exchange platforms, etc.