Block Incremental Dense Tucker Decomposition with Application to Spatial and Temporal Analysis of Air Quality Data

How can we efficiently store and mine dynamically generated dense tensors for modeling the behavior of multidimensional dynamic data?Much of the multidimensional dynamic data in the real world is generated in the form of time-growing tensors.For example,air quality tensor data consists of multiple sensory values gathered from wide locations for a long time.Such data,accumulated over time,is redundant and consumes a lot ofmemory in its raw form.We need a way to efficiently store dynamically generated tensor data that increase over time and to model their behavior on demand between arbitrary time blocks.To this end,we propose a Block IncrementalDense Tucker Decomposition(BID-Tucker)method for efficient storage and on-demand modeling ofmultidimensional spatiotemporal data.Assuming that tensors come in unit blocks where only the time domain changes,our proposed BID-Tucker first slices the blocks into matrices and decomposes them via singular value decomposition(SVD).The SVDs of the time×space sliced matrices are stored instead of the raw tensor blocks to save space.When modeling from data is required at particular time blocks,the SVDs of corresponding time blocks are retrieved and incremented to be used for Tucker decomposition.The factor matrices and core tensor of the decomposed results can then be used for further data analysis.We compared our proposed BID-Tucker with D-Tucker,which our method extends,and vanilla Tucker decomposition.We show that our BID-Tucker is faster than both D-Tucker and vanilla Tucker decomposition and uses less memory for storage with a comparable reconstruction error.We applied our proposed BID-Tucker to model the spatial and temporal trends of air quality data collected in South Korea from 2018 to 2022.We were able to model the spatial and temporal air quality trends.We were also able to verify unusual events,such as chronic ozone alerts and large fire events.

Natural variation of hormone levels in Arabidopsis roots and correlations with complex root architecture

Studies on natural variation are an important tool to unravel the genetic basis of quantitative traits in plants. Despite the significant roles of phytohormones in plant development, including root architecture, hardly any studies have been done to investigate natural variation in endogenous hormone levels in plants. Therefore, in the present study a range of hormones were quantified in root extracts of thirteen Arabidopsis thaliana accessions using a ultra performance liquid chromatography triple quadrupole mass spectrometer. Root system architecture of the set of accessions was quantified, using a new parameter （mature root unit） for complex root systems, and correlated with the phytohormone data. Significant variations in phytohormone levels among the accessions were detected, but were remarkably small, namely less than three-fold difference between extremes. For cytokinins, relatively larger variations were found for ribosides and glucosides, as compared to the free bases. For root phenotyping, length-related traits--lateral root length and total root length--showed larger variations than lateral root number-related ones. For root architecture, antagonistic interactions between hormones, for example, indole-3-acetic acid to trans-zeatin were detected in correlation analysis. These findings provide conclusive evidence for the presence of natural variation in phytohormone levels in Arabidopsis roots, suggesting that quantitative genetic analyses are feasible.