Zipf’s Law Arises Naturally When There Are Underlying, Unobserved Variables

Aitchison, Laurence; Corradi, Nicola; Latham, Peter E.

doi:10.1371/journal.pcbi.1005110

Cited by 79 publications

(114 citation statements)

References 30 publications

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“…Consistent with Zipf's law, the power-law distribution of transcript abundance [162,163], the top 200 expressed transcripts in the bulk RNA-seq data contribute around 50% of the total detected transcripts in the scRNA-seq data and it is clear that these are the only transcripts detected reliably ( Table S5). The abundant transcripts in bulk RNA-seq include many cell type-specific surface markers which explains the ability to use scRNA-seq to discover such markers.…”

Section: The Relationship Between Single Cell and Bulk Rna-seq Datasupporting

confidence: 53%

Transcriptional network analysis of transcriptomic diversity in resident tissue macrophages and dendritic cells in the mouse mononuclear phagocyte system

Hume

2020

Preprint

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The mononuclear phagocyte system (MPS) is a family of cells including progenitors, circulating blood monocytes, resident tissue macrophages and dendritic cells (DC) present in every tissue in the body. To test the relationships between markers and transcriptomic diversity in the MPS, we collected from NCBI-GEO >500 quality RNA-seq datasets generated from mouse MPS cells isolated from multiple tissues. The primary data were randomly down-sized to a depth of 10 million reads and requantified. The resulting dataset was clustered using the network analysis tool Graphia. A sample-to-sample matrix revealed that MPS populations could be separated based upon tissue of origin. Cells identified as classical DC subsets, cDC1 and cDC2, and lacking Fcgr1 (CD64), were centrally-located within the MPS cluster and no more distinct than other MPS cell types. A gene-to-gene correlation matrix identified large generic co-expression clusters associated with MPS maturation and innate immune function. Smaller co-expression clusters including the transcription factors that drive them showed higher expression within defined isolated cells, including macrophages and DC from specific tissues. They include a cluster containing Lyve1 that implies a function in endothelial cell homeostasis, a cluster of transcripts enriched in intestinal macrophages and a generic cDC cluster associated with Ccr7. However, transcripts encoding many other putative MPS subset markers including Adgre1, Itgax, Itgam, Clec9a, Cd163, Mertk, Retnla and H2-A/E (class II MHC) clustered idiosyncratically and were not correlated with underlying functions. The data provide no support for the concept of markers of M2 polarization or the specific adaptation of DC to present antigen to T cells. Co-expression of immediate early genes (e.g. Egr1, Fos, Dusp1) and inflammatory cytokines and chemokines (Tnf, Il1b, Ccl3/4) indicated that all tissue disaggregation protocols activate MPS cells. Tissue-specific expression clusters indicated that all cell isolation procedures also co-purify other unrelated cell types that may interact with MPS cells in vivo. Comparative analysis of public RNA-seq and single cell RNA-seq data from the same lung cell populations showed that the extensive heterogeneity implied by the global cluster analysis may be even greater at a single cell level with few markers strongly correlated with each other. This analysis highlights the power of large datasets to identify the diversity of MPS cellular phenotypes, and the limited predictive value of surface markers to define lineages, functions or subpopulations.

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Section: The Relationship Between Single Cell and Bulk Rna-seq Datasupporting

confidence: 53%

Transcriptional network analysis of transcriptomic diversity in resident tissue macrophages and dendritic cells in the mouse mononuclear phagocyte system

Hume

2020

Preprint

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“…It is curious that Zipf's Law (Zipf 1935), most commonly associated with linguistics, works well for exoplanet multiplicities. Zipfian laws are argued by Aitchison et al (2016) to be natural outcomes of systems involving a large number of latent variables, and this may represent another example. Extending our analysis to M-dwarfs, particularly from TESS, will provide a good test as to whether the Zipfian model can persist in the face of new data.…”

Section: Discussionmentioning

confidence: 99%

The multiplicity distribution of Kepler’s exoplanets

Sandford

Kipping

Collins

2019

Monthly Notices of the Royal Astronomical Society

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The true multiplicity distribution of transiting planet systems is obscured by strong observational biases, leading low-multiplicity systems to be overrepresented in the observed sample. Using the Kepler FGK planet hosts, we employ approximate Bayesian computation to infer the multiplicity distribution by comparing simulated catalogs to the observed one. After comparing a total of ten different multiplicity distributions, half of which were two-population models, to the observed data, we find that a singlepopulation model following a Zipfian distribution is able to explain the Kepler data as well as any of the dichotomous models we test. Our work provides another example of a way to explain the observed Kepler multiplicities without invoking a dichotomous planet population. Using our preferred Zipfian model, we estimate that an additional 2393 +904 −717 planets likely reside in the 1537 FGK Kepler systems studied in this work, which would increase the planet count by a factor of 2.22 +0.46 −0.36 . Of these hidden worlds, 663 +158 −151 are expected to reside in ostensibly single-transiting-planet systems, meaning that an additional planet(s) is expected for approximately 1-in-2 such Kepler systems.

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“…Of course, the knowledge thatŝ comes from a given distribution p(s|θ) changes considerably the picture 9 . In that case, the information that the sampleŝ contains on the generative 9 Even the presence of a structure in the data points provides useful information beyond what is assumed in our general setting. For example, if s = (σ 1 , .…”

Section: Relation With Parametric Modelsmentioning

confidence: 99%

Statistical criticality arises in most informative representations

Cubero

Marsili

et al. 2019

J. Stat. Mech.

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We show that statistical criticality, i.e. the occurrence of power law frequency distributions, arises in samples that are maximally informative about the underlying generating process. In order to reach this conclusion, we first identify the frequency with which different outcomes occur in a sample, as the variable carrying useful information on the generative process. The entropy of the frequency, that we call relevance, provides an upper bound to the number of informative bits. This differs from the entropy of the data, that we take as a measure of resolution. Samples that maximise relevance at a given resolution -that we call maximally informative samples -exhibit statistical criticality. In particular, Zipf's law arises at the optimal trade-off between resolution (i.e. compression) and relevance. As a byproduct, we derive a bound of the maximal number of parameters that can be estimated from a dataset, in the absence of prior knowledge on the generative model. Furthermore, we relate criticality to the statistical properties of the representation of the data generating process. We show that, as a consequence of the concentration property of the Asymptotic Equipartition Property, representations that are maximally informative about the data generating process are characterised by an exponential distribution of energy levels. This arises from a principle of minimal entropy, that is conjugate of the maximum entropy principle in statistical mechanics. This explains why statistical criticality requires no parameter fine tuning in maximally informative samples.When data are generated as independent draws from a parametric distribution, one can draw a sharp distinction between noise and useful information, that part of the data that can be used to estimate the generative model. Useful information is concentrated in sufficient statistics, which are those variables whose empirical value suffices to fully estimate the model's parameter [1]. The first aim of this paper is to draw the same distinction in the case where the model is not known. In this case, we show that the information on the 1 arXiv:1808.00249v5 [physics.data-an]

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Zipf’s Law Arises Naturally When There Are Underlying, Unobserved Variables

Cited by 79 publications

References 30 publications

Transcriptional network analysis of transcriptomic diversity in resident tissue macrophages and dendritic cells in the mouse mononuclear phagocyte system

Transcriptional network analysis of transcriptomic diversity in resident tissue macrophages and dendritic cells in the mouse mononuclear phagocyte system

The multiplicity distribution of Kepler’s exoplanets

Statistical criticality arises in most informative representations

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