A Digital Mass Spectrometer

1971 ◽  
Vol 49 (8) ◽  
pp. 956-965 ◽  
Author(s):  
G. L. Cumming ◽  
M. D. Burke ◽  
F. Tsong ◽  
H. McCullough
Keyword(s):  
Time Series ◽  
Mass Spectrum ◽  
Standard Deviation ◽  
Mass Spectrometer ◽  
Magnetic Tape ◽  
Recording System ◽  
New Method ◽  
Digital Output ◽  
Similar Time ◽  
Spectral Content

A mass spectrometer control and recording system has been built which utilizes synchronous incremental stepping of the magnet current during the scanning of the mass spectrum with time-locked digitizing of the output, producing successive scans as similar time series and preserving the frequency spectral content of each scan. The digital output is recorded on magnetic tape and processed later on a computer. A new method of fitting polynomials to the reduced peak heights is described, which yields a measuring precision of about 0.06% at one standard deviation on 10–20 scans of the spectrum.Some studies of fractionation are described which illustrate the large errors which may occur from this effect.

scholarly journals The Systematic Bias of Entropy Calculation in the Multi-Scale Entropy Algorithm

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 659
Author(s):  
Jue Lu ◽  
Ze Wang
Keyword(s):  
Time Series ◽  
Standard Deviation ◽  
Coarse Graining ◽  
Sample Entropy ◽  
Systematic Bias ◽  
Original Time Series ◽  
Multi Scale ◽  
Calculation Results ◽  
Surrogate Measure ◽  
Original Time

Entropy indicates irregularity or randomness of a dynamic system. Over the decades, entropy calculated at different scales of the system through subsampling or coarse graining has been used as a surrogate measure of system complexity. One popular multi-scale entropy analysis is the multi-scale sample entropy (MSE), which calculates entropy through the sample entropy (SampEn) formula at each time scale. SampEn is defined by the “logarithmic likelihood” that a small section (within a window of a length m) of the data “matches” with other sections will still “match” the others if the section window length increases by one. “Match” is defined by a threshold of r times standard deviation of the entire time series. A problem of current MSE algorithm is that SampEn calculations at different scales are based on the same matching threshold defined by the original time series but data standard deviation actually changes with the subsampling scales. Using a fixed threshold will automatically introduce systematic bias to the calculation results. The purpose of this paper is to mathematically present this systematic bias and to provide methods for correcting it. Our work will help the large MSE user community avoiding introducing the bias to their multi-scale SampEn calculation results.

scholarly journals Distance variable improvement of time-series big data stream evaluation

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Ari Wibisono ◽  
Petrus Mursanto ◽  
Jihan Adibah ◽  
Wendy D. W. T. Bayu ◽  
May Iffah Rizki ◽  
...  
Keyword(s):  
Time Series ◽  
Standard Deviation ◽  
Standard Method ◽  
Time Series Data ◽  
Series Data ◽  
Percentage Error ◽  
Traffic Demand ◽  
Incremental Model ◽  
Chernoff Bound ◽  
The Mean

Abstract Real-time information mining of a big dataset consisting of time series data is a very challenging task. For this purpose, we propose using the mean distance and the standard deviation to enhance the accuracy of the existing fast incremental model tree with the drift detection (FIMT-DD) algorithm. The standard FIMT-DD algorithm uses the Hoeffding bound as its splitting criterion. We propose the further use of the mean distance and standard deviation, which are used to split a tree more accurately than the standard method. We verify our proposed method using the large Traffic Demand Dataset, which consists of 4,000,000 instances; Tennet’s big wind power plant dataset, which consists of 435,268 instances; and a road weather dataset, which consists of 30,000,000 instances. The results show that our proposed FIMT-DD algorithm improves the accuracy compared to the standard method and Chernoff bound approach. The measured errors demonstrate that our approach results in a lower Mean Absolute Percentage Error (MAPE) in every stage of learning by approximately 2.49% compared with the Chernoff Bound method and 19.65% compared with the standard method.

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