Abstract: We introduce an algorithm for synthesizing and verifying piecewise linear Lyapunov functions to prove global exponential stability of piecewise linear dynamical systems. The Lyapunov ...

Understanding a linear function graph is fundamental to grasping core mathematical concepts and their real-world applications. By analyzing the visual representation of a linear equation, we can ...

Abstract: Graph signals are signals with an irregular structure that can be described by a graph. Graph neural networks (GNNs) are information processing architectures tailored to these graph signals ...

In-context learning (ICL) enables LLMs to adapt to new tasks by including a few examples directly in the input without updating their parameters. However, selecting appropriate in-context examples ...

A linear demand curve is a line representing the relationship between the demand for a product or service and its price. Everyone knows that sales are proportional to price: The more you charge for an ...

Department of Systems Biology, Harvard Medical School, Boston, MA, United States The linear framework uses finite, directed graphs with labelled edges to model biomolecular systems. Graph vertices ...

When learning algebra, one of the most crucial skills to acquire is understanding how to graph linear equations. It helps you visualize relationships between variables and solve mathematical problems.

When it comes to teaching mathematics to students, identifying different types of functions can be a challenging task. Two of the most common types of functions encountered in high school math are ...