Dataset Information

The Cluster Structure Function.

ABSTRACT: For each partition of a data set into a given number of parts there is a partition such that every part is as much as possible a good model (an "algorithmic sufficient statistic") for the data in that part. Since this can be done for every number between one and the number of data, the result is a function, the cluster structure function. It maps the number of parts of a partition to values related to the deficiencies of being good models by the parts. Such a function starts with a value at least zero for no partition of the data set and descents to zero for the partition of the data set into singleton parts. The optimal clustering is the one selected by analyzing the cluster structure function. The theory behind the method is expressed in algorithmic information theory (Kolmogorov complexity). In practice the Kolmogorov complexities involved are approximated by a concrete compressor. We give examples using real data sets: the MNIST handwritten digits and the segmentation of real cells as used in stem cell research.

SUBMITTER: Cohen AR

PROVIDER: S-EPMC10525042 | biostudies-literature | 2023 Sep

REPOSITORIES: biostudies-literature

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Publications

The Cluster Structure Function.

Cohen Andrew R AR Vitanyi Paul M B PMB

IEEE transactions on pattern analysis and machine intelligence 20230807 9

For each partition of a data set into a given number of parts there is a partition such that every part is as much as possible a good model (an "algorithmic sufficient statistic") for the data in that part. Since this can be done for every number between one and the number of data, the result is a function, the cluster structure function. It maps the number of parts of a partition to values related to the deficiencies of being good models by the parts. Such a function starts with a value at leas ...[more]

PMID: 37018105

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Project description:Tendons play a critical role in the transmission of forces between muscles and bones, and chronic tendon injuries and diseases are among the leading causes of musculoskeletal disability. For many types of tendinopathies, women have worse clinical outcomes than men. It is possible that sex-based differences in tendon morphology, composition and mechanical properties may explain the greater susceptibility of women to develop tendinopathies. Our objective was to evaluate the mechanical properties, biochemical composition, transcriptome, and cellular activity of plantarflexor tendons from four month old male and female C57Bl/6 mice using in vitro biomechanics, mass spectrometry-based proteomics, genome-wide expression profiling, and cell culture techniques. Differences between groups were tested using t-tests (Î±=0.05). While the Achilles tendons of male mice were approximately 6% larger than female mice (P<0.05), the cell density of female mice was around 19% larger than males (P<0.05). No significant differences in the length (P=0.34), peak force (P=0.86), peak stress (P=0.52) or energy loss during stretch (P=0.94) of plantaris tendons were observed. Mass spectrometry proteomics analysis revealed no significant difference between sexes in the abundance of major extracellular matrix (ECM) proteins like collagen types I (P=0.30) and III (P=0.68), but female mice had approximately two-fold elevations (P<0.05) in different minor ECM proteins such as fibronectin, periostin, and tenascin. Using microarray analysis, there was no significant differences (P>0.05) in the expression of most major and minor ECM genes, and in the expression of genes involved in tendon fibroblast specification or proliferation. Whole tendon qPCR analysis showed significant expression differences in elastin, scleraxis, and tenomodulin. Cell culture techniques to test the effects of sex-specific extracellular environment on cellular activity show significant differences in gene expression of type I and III collagen, Ki67, scleraxis, and tenomodulin. Histologic analysis demonstrated that males have larger tendon cross-sectional area and lower cell density when compared to females. However, there were no differences between the sexes in the mechanical properties of tendons or in the majority of primary structural extracellular matrix proteins, although elevations were observed in some minor ECM proteins. Microarray analysis also showed no significant sex-based differences in the expression of major genes associated with collagen composition, extracellular components and turnover, and fibroblast proliferation. Cell culture tests of non-autonomous cellular activity show no major signals for ECM synthesis nor fibroblast proliferation. Our results indicate that while male mice expectedly had larger tendons, male and female mice have very similar mechanical properties and biochemical composition, with small increases in minor ECM proteins and proteoglycans in female tendons. The role that these minor ECM proteins and proteoglycans play in tendon repair should be evaluated in future studies. No treatment administered, study done to evaluate normal expression profiles of male and female tenocytes. This analysis is based on a Mouse Gene ST 2.1 strip that was processed in the microarray facility in May 2015 using the wt-pico kit.

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The Cluster Structure Function.

Publications

The Cluster Structure Function.

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