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Related Concept Videos

Graphical Representation of Inequalities01:28

Graphical Representation of Inequalities

The graph of the equation where y equals x squared forms a curve known as a parabola. This curve acts as a boundary in the coordinate plane, dividing it into distinct regions based on the relative position of points.When the equality sign in the equation is replaced with an inequality—such as greater than, less than, greater than or equal to, or less than or equal to—the graphical representation changes from a single curve into a broader shaded area that signifies the set of all points...
Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...
Graphs of Equations in Two Variables01:30

Graphs of Equations in Two Variables

An equation with two variables, typically written in the form y = f(x) or Ax + By = C, describes a relationship between quantities represented by x and y. Each solution to such an equation is an ordered pair (x, y) that satisfies the equation when substituted. These pairs can be represented graphically to understand the variables' relationship visually.A common technique for constructing the graph of a two-variable equation is to create a value table. Begin by choosing several values for the...
Graphs of Two-Variable Functions01:27

Graphs of Two-Variable Functions

A weather map provides a practical example of a function of two variables. Across a wide region such as the United States, temperatures vary from one location to another. Each location can be identified by two geographic coordinates: longitude and latitude. Since a single temperature value is assigned to each coordinate pair, the situation can be represented mathematically as a function with two inputs and one output.In mathematical notation, longitude and latitude can be labeled as x and y,...
Graphs of Functions01:30

Graphs of Functions

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...
Network Covalent Solids02:18

Network Covalent Solids

Network covalent solids contain a three-dimensional network of covalently bonded atoms as found in the crystal structures of nonmetals like diamond, graphite, silicon, and some covalent compounds, such as silicon dioxide (sand) and silicon carbide (carborundum, the abrasive on sandpaper). Many minerals have networks of covalent bonds.
To break or to melt a covalent network solid, covalent bonds must be broken. Because covalent bonds are relatively strong, covalent network solids are typically...

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Related Experiment Videos

Aligning Condensed Graph via Hashing: A New Insight for Federated Graph Learning.

Yeyu Yan, Shuai Zheng, Zhenfeng Zhu

    IEEE Transactions on Pattern Analysis and Machine Intelligence
    |July 9, 2026
    PubMed
    Summary

    HashFGL addresses graph heterogeneity in Federated Graph Learning (FGL) by aligning condensed graphs in a symbiotic space. This approach enhances collaboration among diverse clients, improving FGL performance.

    Related Experiment Videos

    Area of Science:

    • Artificial Intelligence
    • Machine Learning
    • Data Science

    Background:

    • Federated Graph Learning (FGL) enables distributed graph analysis while preserving data privacy.
    • Graph heterogeneity, arising from diverse client models and graph structures, poses a significant challenge to efficient FGL collaboration.

    Purpose of the Study:

    • To propose a novel approach, HashFGL, for heterogeneous Federated Graph Learning.
    • To address the challenge of graph heterogeneity by reframing FGL as a semantic condensed graph alignment problem.

    Main Methods:

    • HashFGL introduces a cross-client symbiotic space for enhanced collaboration.
    • An efficient hash-based semantic encoding strategy models local clients, balancing resilience and consistency.
    • A graph condenser preserves semantics and structure during graph condensation for alignment.

    Main Results:

    • HashFGL effectively alleviates the problem of graph heterogeneity in FGL.
    • Experiments on large-scale graphs demonstrate the efficacy and scalability of the proposed method.
    • The approach shows strong performance under both standard and novel realistic partitioning strategies.

    Conclusions:

    • HashFGL offers a robust solution for Federated Graph Learning in heterogeneous environments.
    • The semantic condensed graph alignment framework provides a new perspective for FGL research.
    • The method demonstrates practical applicability and scalability for real-world FGL scenarios.