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Spark (mathematics)

About: Spark (mathematics) is a research topic. Over the lifetime, 7304 publications have been published within this topic receiving 63322 citations.


Papers
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Journal ArticleDOI
01 Aug 2017
TL;DR: This paper proposes a distributed query framework to process trajectory similarity search over a large set of trajectories and implemented the proposed framework in Spark, a popular distributed data processing engine, by carefully considering different design choices.
Abstract: Mobile and sensing devices have already become ubiquitous. They have made tracking moving objects an easy task. As a result, mobile applications like Uber and many IoT projects have generated massive amounts of trajectory data that can no longer be processed by a single machine efficiently. Among the typical query operations over trajectories, similarity search is a common yet expensive operator in querying trajectory data. It is useful for applications in different domains such as traffic and transportation optimizations, weather forecast and modeling, and sports analytics. It is also a fundamental operator for many important mining operations such as clustering and classification of trajectories. In this paper, we propose a distributed query framework to process trajectory similarity search over a large set of trajectories. We have implemented the proposed framework in Spark, a popular distributed data processing engine, by carefully considering different design choices. Our query framework supports both the Hausdorff distance the Frechet distance. Extensive experiments have demonstrated the excellent scalability and query efficiency achieved by our design, compared to other methods and design alternatives.

106 citations

Journal ArticleDOI
TL;DR: In this article, a numerical model is presented which describes the evolution with time of a short segment of a spark channel in air and its associated acoustic wave, assuming a straight, cylindrical conducting column in which local thermodynamic equilibrium exists at every point.
Abstract: A numerical model is presented which describes the evolution with time of a short segment of a spark channel in air and its associated acoustic wave. The model assumes a straight, cylindrical conducting column in which local thermodynamic equilibrium exists at every point. The electrical energy input to the column is determined by a prescribed electrical current waveform, coupled with a computation of the plasma conductivity. The evolution with time of the conducting column and its surrounding flow field is then found by numerical integration of the equations of gas dynamics. The model employs a realistic equation of state for air at high temperatures, and incorporates kinetic and radiative energy transport processes. It is shown that a satisfactory description of the properties of a spark channel cannot be achieved when radiative transport processes are neglected. The model agrees well with experimental measurements of spark channel radii, temperatures, pressures, and electron densities, and predicts the resultant shock wave strengths closely. The voltage gradients along the spark channel predicted by the model, and the total energy input to the channel, are not as uniformly in agreement with experiment. Possible reasons for these discrepancies are discussed.

106 citations

Journal ArticleDOI
TL;DR: A survey of papers published from 1964 through 1971 on the laser spark in gases is presented in this article, where the authors consider the mechanisms whereby laser radiation breaks down a gas, the influence of the experimental conditions on the breakdown threshold, and the interaction of the spark plasma with the laser radiation.
Abstract: A survey is presented of papers published from 1964 through 1971 on the laser spark in gases. The authors consider the mechanisms whereby laser radiation breaks down a gas, the influence of the experimental conditions on the breakdown threshold, and the interaction of the spark plasma with the laser radiation. The parameters of the plasma during the time it is acted upon by the radiation and after the end of the laser pulse are determined. The possibilities of a number of technical applications of a laser spark in gases are discussed.

106 citations

Posted Content
TL;DR: This paper provides new constructions of frames with the following property: every size-M subcollection of the M-dimensional frame elements is a spanning set, and proves that full spark Parseval frames are dense in the entire set of ParseVal frames.
Abstract: Finite frame theory has a number of real-world applications. In applications like sparse signal processing, data transmission with robustness to erasures, and reconstruction without phase, there is a pressing need for deterministic constructions of frames with the following property: every size-M subcollection of the M-dimensional frame elements is a spanning set. Such frames are called full spark frames, and this paper provides new constructions using the discrete Fourier transform. Later, we prove that full spark Parseval frames are dense in the entire set of Parseval frames, meaning full spark frames are abundant, even if one imposes an additional tightness constraint. Finally, we prove that testing whether a given matrix is full spark is hard for NP under randomized polynomial-time reductions, indicating that deterministic full spark constructions are particularly significant because they guarantee a property which is otherwise difficult to check.

105 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202210
2021429
2020525
2019661
2018758
2017683