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 ...

All quadratic functions have the same type of curved graphs with a line of symmetry. The graph of the quadratic function \(y = ax^2 + bx + c \) has a minimum turning point when \(a \textgreater 0 \) ...

In this paper, we unify the Markov theory of a variety of different types of graphs used in graphical Markov models by introducing the class of loopless mixed graphs, and show that all independence ...

Abstract: We study the Fourier dimensions of graphs of real-valued functions defined on the unit interval [0,1]. Our results imply that the graph of fractional Brownian motion is almost surely not a ...