Article history: Received 29 June 2010 Received in final revised form 9 September 2010 Available online 30 October 2010

This paper deals with the number of subgroups of a given exponent in a finite abelian group. Explicit formulas are obtained in the case of rank two and rank three abelian groups. An asymptotic formula is also presented.

The problem of hypothesis testing against independence for a Gauss-Markov random field (GMRF) is analyzed. Assuming an acyclic dependency graph, a closed-form expression for the log-likelihood ratio is derived, in terms of the coefficients of its covariance matrix and the edges of the dependency graph. Assuming random placement of nodes over a large region according to the Poisson or uniform di...

The literature on sparse recovery often adopts the `p “norm” (p ∈ [0, 1]) as the penalty to induce sparsity of the signal satisfying an underdetermined linear system. The performance of the corresponding `p minimization problem can be characterized by its null space constant. In spite of the NP-hardness of computing the constant, its properties can still help in illustrating the performance of ...

We study the zero-temperature phase transitions of a two-dimensional disordered boson Hubbard model at incommensurate boson densities. Via matrix diagonalization and quantum Monte Carlo simulations, we construct the phase diagram and evaluate the correlation length exponent n . In the presence of weak disorder, we obtain n50.560.1, the same value as that in the pure model, near the tip of a Mot...

The sensitivity of trajectories over finite-time intervals t to perturbations of the initial conditions can be associated with a finite-time Lyapunov exponent lambda, obtained from the elements M(ij) of the stability matrix M. For globally chaotic dynamics, lambda tends to a unique value (the usual Lyapunov exponent lambda(infinity)) for almost all trajectories as t is sent to infinity, but for...

We consider the properties of finite isotropic antiferromagnetic Heisenberg chains with S = 1/2, 1, 3/2 spins when a weak magnetic field is applied on a few sites, using White's density matrix renormalization group (DMRG) method. For the S = 1 chain there exists only one length scale in the system which determines the behavior of the one-and two-point correlation functions both around the local...

The Cohn-Umans group-theoretic approach to matrix multiplication suggests embedding matrix multiplication into group algebra multiplication, and bounding $\omega$ in terms of the representation theory of the host group. This framework is general enough to capture the best known upper bounds on $\omega$ and is conjectured to be powerful enough to prove $\omega = 2$, although finding a suitable g...

We investigate the laws that rule the behavior of the largest Lyapunov exponent (LLE) in many particle systems with long-range interactions. We consider as a representative system the so-called Hamiltonian alpha-XY model where the adjustable parameter alpha controls the range of the interactions of N ferromagnetic spins in a lattice of dimension d. In previous work the dependence of the LLE wit...