Morning surface temperature inversions (MSTIS) from Allegheny County,PA to Beijing, China: formation factors, health effects, and applications

In recent years, concern about air quality has increased as we better understand the relationship between air pollution and health, not only of humans and animals but also of the environment. This essay looks at the ways that scientists categorize air pollution as well as the types of air pollution and explores some of the health effects of exposure to air pollutants. Morning surface temperature inversions (MSTIs) are described and how air dispersion conditions might elevate the severity and duration of air pollution is explored. A method to use MSTIs to forecast potentially dangerous air pollution, developed in Allegheny County, Pennsylvania, is applied to data in Beijing, China, an approach that is supported by the similar geographical and environmental conditions the two regions share. This paper only utilizes the MSTIs detecting method, part of the entire forecasting method, to test preliminarily if the method is applicable to Beijing, China. The emergency heavy pollution alerts in Beijing was introduced in this paper, as a potential application field for MSTIs forecasting method in Beijing, China. Results of the preliminary test in Beijing data indicate that there is a promising future for application MSTIs method of Allegheny County to Beijing, China with some criteria adjusted needed to fit Beijing’s situation. A full-time and caliber-consistent equipment is suggested to collect more accurate data for future MSTIs research. Results of the use of the MTSIs method show that some opportunities to warn Beijing residents of potentially dangerous air pollution were missed, and that alerts can sometimes be issued when none is warranted. Public Health Statement: Information sharing is one way that governments can help protect the health of their citizens; establishing policies that limit polluting emissions is another

Robust Time Series Chain Discovery with Incremental Nearest Neighbors

Time series motif discovery has been a fundamental task to identify meaningful repeated patterns in time series. Recently, time series chains were introduced as an expansion of time series motifs to identify the continuous evolving patterns in time series data. Informally, a time series chain (TSC) is a temporally ordered set of time series subsequences, in which every subsequence is similar to the one that precedes it, but the last and the first can be arbitrarily dissimilar. TSCs are shown to be able to reveal latent continuous evolving trends in the time series, and identify precursors of unusual events in complex systems. Despite its promising interpretability, unfortunately, we have observed that existing TSC definitions lack the ability to accurately cover the evolving part of a time series: the discovered chains can be easily cut by noise and can include non-evolving patterns, making them impractical in real-world applications. Inspired by a recent work that tracks how the nearest neighbor of a time series subsequence changes over time, we introduce a new TSC definition which is much more robust to noise in the data, in the sense that they can better locate the evolving patterns while excluding the non-evolving ones. We further propose two new quality metrics to rank the discovered chains. With extensive empirical evaluations, we demonstrate that the proposed TSC definition is significantly more robust to noise than the state of the art, and the top ranked chains discovered can reveal meaningful regularities in a variety of real world datasets

Robust Time Series Chain Discovery with Incremental Nearest Neighbors

Time series motif discovery has been a fundamental task to identify meaningful repeated patterns in time series. Recently, time series chains were introduced as an expansion of time series motifs to identify the continuous evolving patterns in time series data. Informally, a time series chain (TSC) is a temporally ordered set of time series subsequences, in which every subsequence is similar to the one that precedes it, but the last and the first can be arbitrarily dissimilar. TSCs are shown to be able to reveal latent continuous evolving trends in the time series, and identify precursors of unusual events in complex systems. Despite its promising interpretability, unfortunately, we have observed that existing TSC definitions lack the ability to accurately cover the evolving part of a time series: the discovered chains can be easily cut by noise and can include non-evolving patterns, making them impractical in real-world applications. Inspired by a recent work that tracks how the nearest neighbor of a time series subsequence changes over time, we introduce a new TSC definition which is much more robust to noise in the data, in the sense that they can better locate the evolving patterns while excluding the non-evolving ones. We further propose two new quality metrics to rank the discovered chains. With extensive empirical evaluations, we demonstrate that the proposed TSC definition is significantly more robust to noise than the state of the art, and the top ranked chains discovered can reveal meaningful regularities in a variety of real world datasets.Comment: Accepted to ICDM 2022. This is an extended version of the pape

PMP: Privacy-Aware Matrix Profile against Sensitive Pattern Inference

Recent rapid development of sensor technology has allowed massive fine-grained time series (TS) data to be collected and set the foundation for the development of data-driven services and applications. During the process, data sharing is often involved to allow the third-party modelers to perform specific time series data mining (TSDM) tasks based on the need of data owner. The high resolution of TS brings new challenges in protecting privacy. While meaningful information in high-resolution TS shifts from concrete point values to local shape-based segments, numerous research have found that long shape-based patterns could contain more sensitive information and may potentially be extracted and misused by a malicious third party. However, the privacy issue for TS patterns is surprisingly seldom explored in privacy-preserving literature. In this work, we consider a new privacy-preserving problem: preventing malicious inference on long shape-based patterns while preserving short segment information for the utility task performance. To mitigate the challenge, we investigate an alternative approach by sharing Matrix Profile (MP), which is a non-linear transformation of original data and a versatile data structure that supports many data mining tasks. We found that while MP can prevent concrete shape leakage, the canonical correlation in MP index can still reveal the location of sensitive long pattern. Based on this observation, we design two attacks named Location Attack and Entropy Attack to extract the pattern location from MP. To further protect MP from these two attacks, we propose a Privacy-Aware Matrix Profile (PMP) via perturbing the local correlation and breaking the canonical correlation in MP index vector. We evaluate our proposed PMP against baseline noise-adding methods through quantitative analysis and real-world case studies to show the effectiveness of the proposed method

Existence of effective burning velocity in cellular flow for curvature G-equation

G-equation is a popular level set model in turbulent combustion, and becomes an advective mean curvature type evolution equation when curvature of a moving flame in a fluid flow is considered: $$G_t + \left(1-d\, \mathrm{Div}\left({\frac{DG}{|DG|}}\right)\right)_+|DG|+V(x)\cdot DG=0.$$ Here $d>0$ is the Markstein number and the positive part $()_+$ is imposed to avoid negative laminar flame speed that is non-physical. Assume that $V:\mathbb{R}^2\to \mathbb{R}^2$ is a typical steady two dimensional cellular flow, e.g, $V(x)=A\,(DH(x))^{\perp}$ for the stream function $H(x_1,x_2)=\sin (x_1)\sin(x_2)$ and any flow intensity $A>0$. We prove that for any unit vector $p\in \mathbb{R}^2$, $$\left|G(x,t)-p\cdot x+\overline H_A(p)t\right|\leq C \quad \text{in $\mathbb{R}^2\times [0,\infty)$}$$ for a constant $C$ depending only on $d$ and $V$ when $G(x,0)=p\cdot x$. The effective Hamiltonian $\overline H_{A}(p)$ corresponds to the effective burning velocity (turbulent flame speed) in physics literature, which we conjecture to grow like $O\left({A\over \log A}\right)$ as $A$ increases. Our proof combines PDE methods with a dynamical analysis of the Kohn-Serfaty deterministic game characterization of the curvature G-equation while utilizing the special structure of the cellular flow