English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Unambiguous detection of signals superimposed on unknown trends is difficultfor unevenly spaced data. Here, we formulate the Discrete Chi-square Method(DCM) that can determine the best model for many signals superimposed onarbitrary polynomial trends. DCM minimizes the Chi-square for the data in themulti-dimensional tested frequency space. The required number of testedfrequency combinations remains manageable, because the method test statistic issymmetric in this tested frequency space. With our known tested constantfrequency grid values, the non-linear DCM model becomes linear, and all resultsbecome unambiguous. We test DCM with simulated data containing differentmixtures of signals and trends. DCM gives unambiguous results, if the signalfrequencies are not too close to each other, and none of the signals is tooweak. It relies on brute computational force, because all possible freeparameter combinations for all reasonable linear models are tested. DCM workslike winning a lottery by buying all lottery tickets. Anyone can reproduce allour results with the DCM computer code. All files, variables and other programcode related items are printed in magenta colour. Our Appendix gives detailedinstructions for using dcm.py. We also present one preliminary real use case,where DCM is applied to the observed (O) minus the computed (C) eclipse epochsof a binary star, XZ And. This DCM analysis reveals evidence for the possiblepresence of a third and a fourth body in this system. One recent study of avery large sample of binary stars indicated that the probability for detectinga fourth body from the O-C data of eclipsing binaries is only about 0.00005.

Discrete Chi-square Method for Detecting Many Signals