Two statistical validation methods were used to evaluate the confidence level of the Total Column Ozone (TCO) measurements recorded by satellite systems measuring simultaneously, one using the normal distribution and ...Two statistical validation methods were used to evaluate the confidence level of the Total Column Ozone (TCO) measurements recorded by satellite systems measuring simultaneously, one using the normal distribution and another using the Mann-Whitney test. First, the reliability of the TCO measurements was studied hemispherically. While similar coincidences and levels of significance > 0.05 were found with the two statistical tests, an enormous variability in the levels of significance throughout the year was also exposed. Then, using the same statistical comparison methods, a latitudinal study was carried out in order to elucidate the geographical distribution that gave rise to this variability. Our study reveals that between the TOMS and OMI measurements in 2005 there was only a coincidence in 50% of the latitudes, which explained the variability. This implies that for 2005, the TOMS measurements are not completely reliable, except between the -50° and -15° latitude band in the southern hemisphere and between +15° and +50° latitude band in the northern hemisphere. In the case of OMI-OMPS, we observe that between 2011 and 2016 the measurements of both satellite systems are reasonably similar with a confidence level higher than 95%. However, in 2017 a band with a width of 20° latitude centered on the equator appeared, in which the significance levels were much less than 0.05, indicating that one of the measurement systems had begun to fail. In 2018, the fault was not only located in the equator, but was also replicated in various bands in the Southern Hemisphere. We interpret this as evidence of irreversible failure in one of the measurement systems.展开更多
Background:Since biological systems are complex and often involve multiple types of genomic relationships,tensor analysis methods can be utilized to elucidate these hidden complex relationships.There is a pressing nee...Background:Since biological systems are complex and often involve multiple types of genomic relationships,tensor analysis methods can be utilized to elucidate these hidden complex relationships.There is a pressing need for this,as the interpretation of the results of high-throughput experiments has advanced at a much slower pace than the accumulation of data.Results:In this review we provide an overview of some tensor analysis methods for biological systems.Conclusions:Tensors are natural and powerful generalizations of vectors and matrices to higher dimensions and play a fundamental role in physics,mathematics and many other areas.Tensor analysis methods can be used to provide the foundations of systematic approaches to distinguish significant higher order correlations among the elements of a complex systems via finding ensembles of a small number of reduced systems that provide a concise and representative summary of these correlations.展开更多
文摘Two statistical validation methods were used to evaluate the confidence level of the Total Column Ozone (TCO) measurements recorded by satellite systems measuring simultaneously, one using the normal distribution and another using the Mann-Whitney test. First, the reliability of the TCO measurements was studied hemispherically. While similar coincidences and levels of significance > 0.05 were found with the two statistical tests, an enormous variability in the levels of significance throughout the year was also exposed. Then, using the same statistical comparison methods, a latitudinal study was carried out in order to elucidate the geographical distribution that gave rise to this variability. Our study reveals that between the TOMS and OMI measurements in 2005 there was only a coincidence in 50% of the latitudes, which explained the variability. This implies that for 2005, the TOMS measurements are not completely reliable, except between the -50° and -15° latitude band in the southern hemisphere and between +15° and +50° latitude band in the northern hemisphere. In the case of OMI-OMPS, we observe that between 2011 and 2016 the measurements of both satellite systems are reasonably similar with a confidence level higher than 95%. However, in 2017 a band with a width of 20° latitude centered on the equator appeared, in which the significance levels were much less than 0.05, indicating that one of the measurement systems had begun to fail. In 2018, the fault was not only located in the equator, but was also replicated in various bands in the Southern Hemisphere. We interpret this as evidence of irreversible failure in one of the measurement systems.
文摘Background:Since biological systems are complex and often involve multiple types of genomic relationships,tensor analysis methods can be utilized to elucidate these hidden complex relationships.There is a pressing need for this,as the interpretation of the results of high-throughput experiments has advanced at a much slower pace than the accumulation of data.Results:In this review we provide an overview of some tensor analysis methods for biological systems.Conclusions:Tensors are natural and powerful generalizations of vectors and matrices to higher dimensions and play a fundamental role in physics,mathematics and many other areas.Tensor analysis methods can be used to provide the foundations of systematic approaches to distinguish significant higher order correlations among the elements of a complex systems via finding ensembles of a small number of reduced systems that provide a concise and representative summary of these correlations.
