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Related Concept Videos

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The divergence of a vector field at a point is the net outward flow of the flux out of a small volume through a closed surface enclosing the volume, as the volume tends to zero. More practically, divergence measures how much a vector field spreads out or diverges from a given point. For an outgoing flux, conventionally, the divergence is positive. The diverging point is often called the "source" of the field. Meanwhile, the negative divergence of a vector field at a point means that the vector...
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The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write...
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The seminal work of Ohno in 1970 popularized the idea of gene duplication and divergence. DNA sequence comparison studies reveal that a large portion of the genes in bacteria, archaebacteria, and eukaryotes was  generated by gene duplication and divergence, indicating its critical role in evolution.
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The divergence of a vector is a measure of how much the vector spreads out (diverges) from a point. For example, an electric field vector diverges from the positive charge and converges at the negative charge. The divergence of an electric field is derived using Gauss's law and is equal to the charge density divided by the permittivity of space. Mathematically, it is expressed as
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Digitizing omics profiles by divergence from a baseline.

Wikum Dinalankara1, Qian Ke2, Yiran Xu2

  • 1Department of Oncology, Johns Hopkins University School of Medicine, Baltimore, MD 21205.

Proceedings of the National Academy of Sciences of the United States of America
|April 19, 2018
PubMed
Summary
This summary is machine-generated.

This study introduces a new bioinformatics theory to quantify molecular differences in individual samples, moving beyond population averages. This approach enables personalized analysis of gene expression and pathway dysregulation for better disease understanding.

Keywords:
cancerdigitizationdysregulationprecision medicinestochasticity

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Area of Science:

  • Bioinformatics
  • Computational Biology
  • Genomics

Background:

  • Omics technologies reveal significant molecular heterogeneity between individual samples, even within the same disease subtype.
  • Existing bioinformatics methods, like differential gene expression analysis, are population-based and fail to capture this inter-sample diversity.
  • This limitation hinders personalized medicine and a deep understanding of biological variation.

Purpose of the Study:

  • To develop a unified theory for quantifying sample-level heterogeneity in omics data.
  • To enable the analysis of molecular dysregulation at the individual sample level.
  • To facilitate personalized and biologically interpretable analyses of variation in omics profiles.

Main Methods:

  • A unified theory is proposed to simplify omics profiles into a digital representation based on a reference population.
  • The concept of "divergence" is introduced to identify molecular states outside the baseline distribution, indicating dysregulation.
  • Analysis is performed on single features (e.g., genes) and subsets (e.g., pathways).

Main Results:

  • The new theory allows for the quantification of heterogeneity at the individual omics profile level.
  • Dysregulation can be assessed probabilistically, estimating the likelihood of a gene or pathway being divergent.
  • The method reduces complexity, enabling more personalized and interpretable biological variation analysis.

Conclusions:

  • This approach provides a powerful tool for analyzing individual sample heterogeneity in omics data.
  • It supports personalized medicine by enabling a more nuanced understanding of disease states.
  • Applications include tissue characterization, disease detection, progression monitoring, and pathway association studies.