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Related Concept Videos

Dimensional Analysis03:40

Dimensional Analysis

65.0K
Dimensional analysis, also known as the factor label method, is a versatile approach for mathematical operations. The main principle behind this approach is: the units of quantities must be subjected to the same mathematical operations as their associated numbers. This method can be applied to computations ranging from simple unit conversions to more complex and multi-step calculations involving several different quantities and their units.
Conversion Factors and Dimensional Analysis
The unit...
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Dimensional Analysis01:27

Dimensional Analysis

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Dimensional analysis is a valuable technique in fluid mechanics for simplifying complex problems by reducing them into dimensionless groups. These groups capture the essential relationships between the variables involved, allowing researchers and engineers to analyze fluid flow without dealing with each variable individually. This approach reduces the number of independent variables, allowing for easier analysis and better understanding of physical phenomena.
In fluid mechanics, dimensional...
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Dimensional Analysis01:23

Dimensional Analysis

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Dimensional analysis is a powerful tool that is used in physics and engineering to understand and predict the behavior of physical systems. The basic idea behind dimensional analysis is to express physical quantities in terms of fundamental dimensions such as the mass, length, and time. Derived dimensions like the velocity, acceleration, and force are derived from the combinations of these fundamental dimensions.
Dimensional analysis allows us to analyze and compare physical quantities on a...
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Dimensional Analysis02:19

Dimensional Analysis

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The concept of dimension is important because every mathematical equation linking physical quantities must be dimensionally consistent, implying that mathematical equations must meet the following two rules. The first rule is that, in an equation, the expressions on each side of the equal sign must have the same dimensions. This is fairly intuitive since we can only add or subtract quantities of the same type (dimension). The second rule states that, in an equation, the arguments of any of the...
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Genomics02:02

Genomics

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Genomics is the science of genomes: it is the study of all the genetic material of an organism. In humans, the genome consists of information carried in 23 pairs of chromosomes in the nucleus, as well as mitochondrial DNA. In genomics, both coding and non-coding DNA is sequenced and analyzed. Genomics allows a better understanding of all living things, their evolution, and their diversity. It has a myriad of uses: for example, to build phylogenetic trees, to improve productivity and...
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Problem Solving: Dimensional Analysis01:08

Problem Solving: Dimensional Analysis

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Every mathematical equation that connects separate distinct physical quantities must be dimensionally consistent, which implies it must abide by two rules. For this reason, the concept of dimension is crucial. The first rule is that an equation's expressions on either side of an equality must have the exact same dimension, i.e., quantities of the same dimension can be added or removed. The second rule stipulates that all popular mathematical functions, such as exponential, logarithmic, and...
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Related Experiment Video

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ExCYT: A Graphical User Interface for Streamlining Analysis of High-Dimensional Cytometry Data
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A Feature Sampling Strategy for Analysis of High Dimensional Genomic Data.

Jie Zhang, Zhigen Zhao, Kai Zhang

    IEEE/ACM Transactions on Computational Biology and Bioinformatics
    |July 11, 2018
    PubMed
    Summary

    This study introduces a new method for gene selection in high-throughput genomic studies. It effectively identifies highly correlated causal genes, overcoming limitations of existing techniques like lasso regression.

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    Area of Science:

    • Genomics
    • Bioinformatics
    • Statistical Genetics

    Background:

    • High-throughput technology enables simultaneous profiling of tens of thousands of gene activities.
    • Genomic datasets often feature a large number of genes (features) compared to the number of samples.
    • High correlation among genes, especially within the same biological pathways, poses challenges for accurate gene selection.

    Purpose of the Study:

    • To address the limitations of existing variable selection methods, such as lasso regression, in genomic studies.
    • To develop a novel, robust, and stable method for selecting meaningful genes, particularly when dealing with highly correlated candidates.
    • To enable the identification of all causal genes, even when they are highly correlated, which is a common desire in biological research.

    Main Methods:

    • Development of a novel variable selection method designed to overcome lasso regression's limitations.
    • Utilizing simulation studies to evaluate the performance of the proposed method.
    • Applying the method to real-world transcriptome data for validation.

    Main Results:

    • The proposed method demonstrates superior performance in selecting highly correlated causal genes compared to existing techniques.
    • Simulation studies confirm the effectiveness of the new approach.
    • Real-world application on transcriptome data validates the method's practical utility.

    Conclusions:

    • The novel variable selection method is effective and robust for identifying highly correlated causal genes in genomic studies.
    • The method overcomes key limitations of traditional approaches like lasso regression.
    • Theoretical justifications based on mean and variance analyses support the proposed feature sampling strategy.