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Related Concept Videos

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...
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 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...
Observational Learning01:12

Observational Learning

Albert Bandura's observational learning, also known as imitation or modeling, occurs when a person observes and imitates another's behavior. It is a quicker process than operant conditioning. A well-known example is the Bobo doll study, where children who saw an adult acting aggressively towards the doll were more likely to act aggressively when left alone, compared to those who observed a nonaggressive adult. Many psychologists view observational learning as a form of latent learning because...
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,...
State Space Representation01:27

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...

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Related Experiment Videos

Self-Supervised Continuous Dynamic Graph Representation Learning via Hawkes Processes.

Ruyue Liu, Rong Yin, Xingrui Zhou

    IEEE Transactions on Neural Networks and Learning Systems
    |July 1, 2026
    PubMed
    Summary
    This summary is machine-generated.

    Self-supervised dynamic graph representation learning (DGRL) using Hawkes processes improves temporal accuracy without labeled data. This novel framework captures event interactions for efficient, versatile node embeddings, outperforming existing methods.

    Related Experiment Videos

    Area of Science:

    • Machine Learning
    • Graph Neural Networks
    • Temporal Data Analysis

    Background:

    • Dynamic graph representation learning (DGRL) is crucial for real-world applications but often requires costly labeled data.
    • Existing DGRL methods struggle to capture temporal interactions and event persistence, leading to suboptimal representations.
    • The cumulative impact of past events in dynamic graphs can be complex and sequence-dependent.

    Purpose of the Study:

    • To introduce a novel self-supervised framework for dynamic graph representation learning (DGRL).
    • To enhance temporal representations by accurately modeling event interactions, including excitation and inhibition.
    • To develop an efficient and versatile DGRL method that generalizes to various downstream tasks without task-specific encoders.

    Main Methods:

    • Proposed self-supervised dynamic graph representation learning (SDGRL) framework based on Hawkes processes.
    • Leveraged Hawkes processes to model multi-perspective event interactions, capturing temporal dependencies.
    • Demonstrated theoretical properties including stationarity and convergence of the SDGRL method.

    Main Results:

    • SDGRL achieves optimal performance across eight real-world datasets, outperforming nine existing methods.
    • On the Tmall dataset, SDGRL improved inductive dynamic link prediction accuracy by 28.73% compared to DyGFormer.
    • SDGRL significantly reduced computational costs, decreasing time by 1.29x and memory usage by 15.33x.

    Conclusions:

    • SDGRL offers an effective self-supervised approach for DGRL, eliminating the need for labeled data.
    • The framework accurately captures complex temporal event interactions, leading to superior node embeddings.
    • SDGRL provides a computationally efficient and versatile solution for dynamic graph analysis.