106,076 research outputs found
Structural graph matching using the EM algorithm and singular value decomposition
This paper describes an efficient algorithm for inexact graph matching. The method is purely structural, that is, it uses only the edge or connectivity structure of the graph and does not draw on node or edge attributes. We make two contributions: 1) commencing from a probability distribution for matching errors, we show how the problem of graph matching can be posed as maximum-likelihood estimation using the apparatus of the EM algorithm; and 2) we cast the recovery of correspondence matches between the graph nodes in a matrix framework. This allows one to efficiently recover correspondence matches using the singular value decomposition. We experiment with the method on both real-world and synthetic data. Here, we demonstrate that the method offers comparable performance to more computationally demanding method
Stationary waves on nonlinear quantum graphs: General framework and canonical perturbation theory
In this paper we present a general framework for solving the stationary
nonlinear Schr\"odinger equation (NLSE) on a network of one-dimensional wires
modelled by a metric graph with suitable matching conditions at the vertices. A
formal solution is given that expresses the wave function and its derivative at
one end of an edge (wire) nonlinearly in terms of the values at the other end.
For the cubic NLSE this nonlinear transfer operation can be expressed
explicitly in terms of Jacobi elliptic functions. Its application reduces the
problem of solving the corresponding set of coupled ordinary nonlinear
differential equations to a finite set of nonlinear algebraic equations. For
sufficiently small amplitudes we use canonical perturbation theory which makes
it possible to extract the leading nonlinear corrections over large distances.Comment: 26 page
Effective Field Theories
Three lectures on effective field theory given at the Seventh Summer School
in Nuclear Physics, Seattle June 19-30 1995.Comment: 40 pages uuencoded with figures; requires macros harvmac, epsf.te
Renormalization group scaling in nonrelativistic QCD
We discuss the matching conditions and renormalization group evolution of
non-relativistic QCD. A variant of the conventional MS-bar scheme is proposed
in which a subtraction velocity nu is used rather than a subtraction scale mu.
We derive a novel renormalization group equation in velocity space which can be
used to sum logarithms of v in the effective theory. We apply our method to
several examples. In particular we show that our formulation correctly
reproduces the two-loop anomalous dimension of the heavy quark production
current near threshold.Comment: (27 pages, revtex
- …