Blind musicians Blind musicians Blind musicians are singers or instrumentalists, or in some cases singer-accompanists, who are legally blind. Historically, many blind musicians, including some of the most famous, have performed without the benefit of formal instruction, since such instruction relies extensively on written musical notation. However, today there are many resources available for blind musicians who wish to learn Western music theory and classical notation. Louis Braille, the man who created the braille alphabet for the blind, also created a system of classical notation for the blind called Braille music. This system allows the blind to read and write music just
Dot product representation of a graph Dot product representation of a graph A dot product representation of a simple graph is a method of representing a graph using vector spaces and the dot product from linear algebra. Every graph has a dot product representation. Let "G" be a graph with vertex set "V". Let "F" be a field, and "f" a function from "V" to "F" such that "xy" is an edge of "G" if and only if "f"("x")·"f"("y") ≥ "t". This is the dot product representation of "G". The number "t" is called the dot product threshold, and the smallest possible value of "k" is