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Graphs of functions provide a visual representation of how output values change in response to varying inputs. Each point on the graph corresponds to an ordered pair, where the x-coordinate (independent variable) determines the horizontal position and the y-coordinate (dependent variable) determines the vertical position. Linear functions like y = x give a straight line, indicating a constant rate of change.Nonlinear functions display more complex behaviors. Even power functions generate...
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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...
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Sigmund Freud's model of the human psyche is often illustrated using an iceberg analogy. The iceberg's visible tip represents the conscious mind, which includes thoughts and perceptions that individuals are immediately aware of. However, the larger, submerged portion of the iceberg represents the unconscious mind, a reservoir of repressed desires, instincts, and memories. According to Freud, human behavior is primarily shaped by this hidden realm.
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The polar coordinate system represents points using a distance from a central point (the pole) and an angle from a reference direction (the polar axis). Unlike rectangular coordinates, polar coordinates are ideal for graphing curves with radial symmetry or periodic behavior.Some general forms of graphs in polar coordinates include the following:Equation of a Circle (Centered at the Pole):A graph where the radius remains constant for all angles traces a circle centered at the pole:Equation of a...
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The Graph of Our Mind.

Balázs Szalkai1, Bálint Varga1, Vince Grolmusz1,2

  • 1PIT Bioinformatics Group, Eötvös University, H-1117 Budapest, Hungary.

Brain Sciences
|April 3, 2021
PubMed
Summary

Human brain connections, analyzed using graph theory and diffusion MRI, reveal significant sex differences. Female brains exhibit superior network properties, akin to high-performance computer networks.

Area of Science:

  • Neuroscience
  • Graph Theory
  • Network Science

Background:

  • Graph theory has become integral to diverse scientific fields, including human brain connectivity studies.
  • Diffusion MRI enables mapping brain region connections, representing them as complex graphs.
  • The Human Connectome Project provides high-quality data for analyzing brain networks.

Purpose of the Study:

  • To investigate sex-based differences in human brain graph parameters.
  • To compare network properties of male and female brain graphs.
  • To relate brain network characteristics to measures of computer interconnection networks.

Main Methods:

  • Utilized graph theory to analyze brain connectivity data from the Human Connectome Project.
  • Computed 1015-vertex graphs representing brain networks for hundreds of subjects.
Keywords:
braingraphconnectomesex differences

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  • Applied statistical analysis to 116 graph parameters across 426 subjects.

    • Main Results:

    • Identified statistically significant differences in numerous graph parameters between male and female brain graphs.
    • Female braingraphs demonstrated enhanced expansion properties, more edges, larger bipartition widths, and larger vertex covers.
    • These findings were statistically corrected for multiple comparisons.

    Conclusions:

    • Human brain networks exhibit distinct topological properties between sexes.
    • Female brain networks possess characteristics associated with high-quality parallel computer interconnection networks.
    • Graph theory provides a powerful framework for understanding neurobiological sex differences.