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Related Concept Videos

Time-Series Graph00:54

Time-Series Graph

A time-series graph is a line graph with repeated measurements taken at successive intervals of time. It is also called a time series chart. To construct a time-series graph, one must look at both pieces of a paired data set. The horizontal axis is used to plot the time increments, and the vertical axis is used to plot the values of the variable that one is measuring. By using the axes in this way, each point on the graph will correspond to time and a measured quantity. The points on the graph...
Second Derivatives and the Shape of a Graph01:29

Second Derivatives and the Shape of a Graph

The second derivative of a function provides essential information about a graph's curvature and how it changes over an interval. It helps determine whether a function is concave upward or concave downward and identifies points where the curvature changes. These properties are fundamental in analyzing real-world scenarios, such as changes in road elevation, population growth, and economic trends.A function f(x) is considered concave upward on an interval if its graph lies above all its tangent...
First Derivatives and the Shape of a Graph01:22

First Derivatives and the Shape of a Graph

In calculus, the concept of the first derivative plays a crucial role in understanding the behavior of a function over its domain. The first derivative, denoted as f’(x), provides insight into how a function changes at any given point, much like a cyclist adjusting speed along a winding trail. By analyzing the first derivative, mathematicians can determine where a function is increasing, decreasing, or reaching critical points.The first derivative provides a precise method for classifying...
First Derivative Test: Problem Solving01:25

First Derivative Test: Problem Solving

Imagine an asset price that crashes to a low point, rebounds sharply as bargain-hunters step in, and then gradually declines. Such behavior can be modeled with a smooth function whose turning points represent locally overvalued and undervalued regions. A convenient example that captures rebound followed by decay is:The high and low points of this curve are identified using the first derivative test, which determines where the function changes from increasing to decreasing or vice versa. To...
Cluster Sampling Method01:20

Cluster Sampling Method

Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...
Curve Sketching and Derivatives01:22

Curve Sketching and Derivatives

Understanding the behavior of a function through its first and second derivatives is essential for analyzing its graph. Derivatives provide insight into where a function increases or decreases, where it attains local maxima or minima, and how its curvature behaves across different intervals.The first derivative of a function reveals the slope of the tangent line at any given point. Points where the derivative is zero or undefined are considered critical, as they often indicate potential extrema...

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Related Experiment Video

Updated: Jul 12, 2026

Alignment of Synchronized Time-Series Data Using the Characterizing Loss of Cell Cycle Synchrony Model for Cross-Experiment Comparisons
07:59

Alignment of Synchronized Time-Series Data Using the Characterizing Loss of Cell Cycle Synchrony Model for Cross-Experiment Comparisons

Published on: June 9, 2023

Clustering time-series gene expression data using smoothing spline derivatives.

S Déjean1, P G P Martin, A Baccini

  • 1Laboratoire de Statistique et Probabilités, UMR 5583, Université Paul Sabatier, Toulouse Cedex 9, France.

EURASIP Journal on Bioinformatics & Systems Biology
|August 24, 2007
PubMed
Summary

This study analyzed gene expression changes in mice during fasting using advanced clustering methods. The findings reveal temporal gene expression patterns in the mouse liver, aligning with existing research and suggesting new avenues for biological inquiry.

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Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps
11:52

Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps

Published on: February 9, 2017

Related Experiment Videos

Last Updated: Jul 12, 2026

Alignment of Synchronized Time-Series Data Using the Characterizing Loss of Cell Cycle Synchrony Model for Cross-Experiment Comparisons
07:59

Alignment of Synchronized Time-Series Data Using the Characterizing Loss of Cell Cycle Synchrony Model for Cross-Experiment Comparisons

Published on: June 9, 2023

Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps
11:52

Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps

Published on: February 9, 2017

Area of Science:

  • Molecular Biology
  • Systems Biology
  • Bioinformatics

Background:

  • Gene expression analysis using microarrays enables monitoring of temporal variations.
  • Understanding gene expression dynamics is crucial for deciphering biological processes.

Purpose of the Study:

  • To develop a robust method for clustering gene expression temporal profiles.
  • To analyze gene expression changes in mouse liver during a 72-hour fasting period.

Main Methods:

  • Utilized macroarray data from 200 genes across 11 time points during fasting.
  • Combined spline smoothing and first derivative computation with hierarchical and partitioning clustering.
  • Developed a heuristic approach for tuning spline smoothing parameters based on statistical and biological factors.

Main Results:

  • Successfully clustered gene expression profiles based on curve shapes rather than absolute expression levels.
  • Principal Component Analysis (PCA) and heatmap visualization were used to illustrate clusters.
  • Identified temporal gene expression patterns consistent with known effects of fasting on the mouse liver.

Conclusions:

  • The developed clustering approach effectively captures temporal gene expression dynamics.
  • Results provide a foundation for further investigation into fasting-induced molecular mechanisms in the liver.
  • This study offers valuable insights into the temporal regulation of gene expression during metabolic stress.