The statistical physics of graphs and partition functions represents a vibrant intersection of graph theory, statistical mechanics and computational complexity. By summing over an ensemble of ...

Exponential and logarithmic functions are typically presented as formulas with which students learn to associate the rules for exponents/logarithms, a particular algebraic form, and routine algorithms ...

A PHASE relation familiar to students of applied mathematics exists between a simple harmonic oscillation and its derivative. Similar relations exist between exponential functions and their ...

We study the asymptotics for sparse exponential random graph models where the parameters may depend on the number of vertices of the graph. We obtain exact estimates for the mean and variance of the ...