Spatial-temporal Space Research Articles

GraphTS: Graph-represented time series for subsequence anomaly detection.

Automatic detection of subsequence anomalies (i.e., an abnormal waveform denoted by a sequence of data points) in time series is critical in a wide variety of domains. However, most existing methods for subsequence anomaly detection often require knowing the length and the total number of anomalies in time series. Some methods fail to capture recurrent subsequence anomalies due to using only local or neighborhood information for anomaly detection. To address these limitations, in this paper, we propose a novel graph-represented time series (GraphTS) method for discovering subsequence anomalies. In GraphTS, we provide a new concept of time series graph representation model, which represents both recurrent and rare patterns in a time series. Particularly, in GraphTS, we develop a new 2D time series visualization (2Dviz) method, which compacts all 1D time series patterns into a 2D spatial temporal space. The 2Dviz method transfers time series patterns into a higher-resolution plot for easier sequence anomaly recognition (or detecting subsequence anomalies). Then, a Graph is constructed based on the 2D spatial temporal space of time series to capture recurrent and rare subsequence patterns effectively. The represented Graph also can be used to discover single and recurrent subsequence anomalies with arbitrary lengths. Experimental results demonstrate that the proposed method outperforms the state-of-the-art methods in terms of accuracy and efficiency.

Semantic Modeling of Ship Behavior in Cognitive Space

Ship behavior is the semantic expression of corresponding trajectory in spatial-temporal space. The intelligent identification of ship behavior is critical for safety supervision in the waterborne transport. In particular, the complicated behavior reflects the long-term intentions of a ship, but it is challenging to recognize it automatically for computers without a proper understanding. For this purpose, this study provides a method to model the behavior for computers from the perspective of knowledge modeling that is explainable. Based on our previous work, a semantic model for ship behavior representation is given considering the multi-scale features of ship behavior in cognitive space. Firstly, the multi-scale features of ship behavior are analyzed in spatial-temporal dimension and semantic dimension individually. Then, a method for multi-scale behaviors modeling from the perspective of semantics is determined, which divides the behavior scale into four sub-scales in cognitive space, considering spatial and temporal dimensions: action, activity, process, and event. Furthermore, an ontology model is introduced to construct the multi-scale semantic model for ship behavior, where behaviors with different semantic scales are expressed using the functions of ontology from a microscopic perspective to a macroscopic perspective consecutively. To validate the model, a case study is conducted in which ship behavior with different scales occurred in port water areas. Typical behaviors, which include leveraging the axioms expression and semantic web rule language (SWRL) of the ontology, are then deduced using a reasoner, such as Pellet. The results show that the model is reasonable and feasible to represent multi-scale ship behavior in various scenarios and provides the potential to construct a smart supervision network for maritime authorities.

The fusion of flow field data with multiple fidelities

We propose a spatial-temporal multi-fidelity Gaussian process regression framework for the fusion of flow field data with various availabilities and fidelities but not sufficiently large to train neural networks commonly encountered in fluid mechanics studies. For example, fluid experiments lead to data with high fidelity but sparse in time and space, while most of the numerical data are generally regarded as less accurate but are spatially temporally continuous. The proposed framework aims at generating a new set of fused data by combining the merits of those in the spatial-temporal space. Numerical simulations [e.g., direct numerical simulation (DNS), large eddy simulation, Reynolds-averaged Navier–Stokes] of flow around a National Advisory Committee for Aeronautics 0012 airfoil are performed to collect the original raw data with various fidelities, and a fraction of the DNS result is used to mimic the high-fidelity but sparse experimental data. It is found that the accuracy of the fused data increases with the density of high-fidelity points until reaching a threshold, above which the fusion accuracy becomes insensitive. This limit can be overcome by introducing extra dimensions, such as the gradients of the low-fidelity data field. By examining the error fields, it is found that the high-fidelity points can tune low-fidelity fields but only within a limited local region. The accuracy can be firmly improved by introducing more high-fidelity points or higher levels of spatial gradients if the data set captures the temporal development.

Prediction model for the spread of the COVID-19 outbreak in the global environment

COVID-19 has long become a worldwide pandemic. It is responsible for the death of over two million people and posed an economic recession. This paper studies the spread pattern of COVID-19, aiming to establish a prediction model for this event. We harness Data Mining and Machine Learning methodologies to train regression models to predict the number of confirmed cases in a spatial-temporal space. We introduce an innovative concept ‒ the Center of Infection Mass (CoIM) ‒ adapted from the field of physics. We empirically evaluated our model on western European countries, based on the CoIM index and other features, and showed that a relatively high accurate prediction of the spread can be obtained. Our contribution is twofold: first, we introduced a prediction methodology and proved empirically that a prediction can be made even to the range of over a month; second, we showed promise in adopting the CoIM index to prediction models, when models that adopt the CoIM yield significantly better results than those that discard it. By applying our model, and better controlling the inherent tradeoff between life-saving and economy, we believe that decision-makers can take close to optimal measures. Thus, this methodology may contribute to public welfare.

A novel spatial–temporal space heating and hot water demand method for expansion analysis of district heating systems

The fourth generation of district heating will play a significant role in the decarbonization of energy systems. In general, only space heating demand is considered when assessing the district heating potential, excluding hot water. In contrast, the hot water demand accounts for up to 18% of total final energy demand in buildings. Hence, in this paper, a spatial–temporal method for annual hot water demand is considered in conjunction with space heating demand while technically and economically assessing the expansion potential of the district heating. A bottom-up heat demand mapping process was carried out for Pristina city to identify the space heating demand of buildings, while a top-down approach was used for spatial mapping of hot water demand. Hourly, daily, weekly and seasonal hot water demand profiles, besides heating degree-day method used for space heating, were considered when estimating the temporal operation of district heating. The findings show that the existing district heating can be increased four times when excluding hot water and five times when considering both space heating and hot water demand of buildings. Moreover, the heat supply capacities needed in district heating to cover space heating and hot water demand would be 600 MW and 70 MW respectively.

Time series trend detection and forecasting using complex network topology analysis

Extracting knowledge from time series provides important tools for many real applications. However, many challenging problems still open due to the stochastic nature of large amount of time series. Considering this scenario, new data mining and machine learning techniques have continuously developed. In this paper, we study time series based on its topological features, observed on a complex network generated from the time series data. Specifically, we present a trend detection algorithm for stochastic time series based on community detection and network metrics. The proposed model presents some advantages over traditional time series analysis, such as adaptive number of classes with measurable strength and better noise absorption. The appealing feature of this work is to pave a new way to represent time series trends by communities of complex networks in topological space instead of physical space (spatial–temporal space or frequency spectral) as traditional techniques do. Experimental results on artificial and real data-sets shows that the proposed method is able to classify the time series into local and global patterns. As a consequence, it improves the predictability on time series.

Existence of solution to parabolic equations with mixed boundary condition on non-cylindrical domains

In this paper we study the existence of weak solutions to initial boundary value problems of linear and semi-linear parabolic equations with mixed boundary conditions on non-cylindrical domains ⋃t∈(0,T)Ω(t)×{t} of spatial-temporal space RN×R. In the case of the linear equation, each boundary condition is given on any open subset of the boundary surface Σ=⋃t∈(0,T)∂Ω(t)×{t} under a condition that the boundary portion for Dirichlet condition Σ0⊂Σ is nonempty at any time t. Due to this, it is difficult to reduce the problem to the one on a cylindrical domain by diffeomorphism of the spatial domains Ω(t). By a transformation of the unknown function and the penalty method, we connect the problem to a monotone operator equation for functions defined on the non-cylindrical domain. We are also concerned with a semilinear problem when the boundary portion for Dirichlet condition is cylindrical.

A Progressive Search Paradigm for the Internet of Things

As the Internet of Things (IoT) expands, IoT search has tremendous potential applications but also presents many challenges. To solve these challenges, we propose a progressive search paradigm to reduce the search space that has three main strategies: coarse-to-fine search in the feature space, near-to-distant search in the spatial-temporal space, and low-to-high permission search in the security space. Two case studies from a multimedia-based urban sensing network demonstrate that our approach can significantly improve IoT search speed and accuracy.

Statistical properties of a quantum cellular automaton

We study a quantum cellular automaton (QCA) whose time-evolution is defined from global transition function of classical cellular automata (CA). In order to investigate natural transformations from CA to QCA, the present QCA includes CA with Wolfram's rule 150 and 105 as special cases. We firstly compute the time-evolution of the QCA and examine its statistical properties. As a basic statistical value, the probability of finding an active cell averaged over a spatial-temporal space is introduced, and the difference between CA and QCA is considered. In addition, it is shown that statistical properties in QCA are related to the classical trajectory in the configuration space.

On the spatial-temporal averaging method for modeling transport in porous media

The spatial-temporal averaging procedure is considered with a nonhomogeneous distribution of elementary domains in the spatial-temporal space and the probabilistic interpretation of the ST-averaging is also given. Several averaging theorems and corollaries about the averages of spatial and temporal derivatives are presented and rigorously proved which allow elementary domain to vary in space and time. The macroscopic transport equation in the most general condition and the simplified macroscopic equation under the special form of distributions are developed which may be reduced to the classical macroscopic transport equation as the spatial-temporal average degenerates into the volume average.