We calculate the large-q expansion of the second moment correlation length at the first order phase transition point of the q-state Potts model in two dimensions both in the ordered and disordered phases to order 21 in 1/ √ q. They coincide with each other to the third term of the series but differ a little in higher orders. Numerically the ratio of the second moment correlation length in the t...

We present a N-dimensional generalization of the two-dimensional block-circulant perfect array construction by [Blake, 2013]. As in [Blake, 2013], the families of N-dimensional arrays possess pairwise good zero correlation zone (ZCZ) cross-correlation. Both constructions use a perfect autocorre-lation sequence with the array orthogonality property (AOP). This paper presents a generalization of ...

Emphasis is placed on generating space-time trajectories of wind power generation, consisting of paths sampled from high-dimensional joint predictive densities, describing wind power generation at a number of contiguous locations and successive lead times. A modelling approach taking advantage of the sparsity of precision matrices is introduced for the description of the underlying space-time d...

We exhibit a family of infinite, finitely-presented, nilpotent-byabelian groups. Each member of this family is a solvable S-arithmetic group that is related to Baumslag-Solitar groups, and everyone of these groups has a quasi-isometry group that is virtually a product of a solvable real Lie group and a solvable p-adic Lie group. In addition, we propose a candidate for a polycyclic group whose q...

In this paper, we discuss three methods for the computation of the model parameters of spatial channel simulators basing on Rice’s sum of sinusoids. Each method is universally described and can in principle be applied to the modelling of any type of scattering object with given spatial characteristics. However, examples illustrating the procedures are presented for a Laplacian scattering object...

Decreased leaf moisture content, typically measured as equivalent water thickness (EWT), is an early signal of tree stress caused by drought, disease, or pest insects. We investigated the use of two terrestrial laser scanners (TLSs) employing different wavelengths for improving the understanding how EWT can be retrieved in a laboratory setting. Two wavelengths were examined for normalizing the ...

In the general case of multilevel Toeplitz matrices, we recently proved that any multilevel circulant preconditioner is not superlinear (a cluster it may provide cannot be proper). The proof was based on the concept of quasi-equimodular matrices, although this concept does not apply, for example, to the sine-transform matrices. In this paper, with a new concept of partially equimodular matrices...

Measuring the topological overlap of two graphs becomes important when assessing the changes between temporally adjacent graphs in a time-evolving network. Current methods depend on the fraction of nodes that have persisting edges. This breaks down when there are nodes with no edges, persisting or otherwise. The following outlines a proposed correction to ensure that correlation metrics have th...

The Internet is a complex network of interconnected routers, and the existence of a collective behavior such as congestion suggests that the correlations between the different connections play a crucial role. It is thus critical to measure and quantify these correlations. We use methods of random matrix theory (RMT) to analyze the cross-correlation matrix C of information flow changes of 650 co...

In this paper we study the super-critical 2D dissipative quasi-geostrophic equation. We obtain some regularization effects allowing us to prove global well-posedness result for small initial data lying in critical Besov spaces constructed over Lebesgue spaces L, with p ∈ [1,∞]. Local results for arbitrary initial data are also given.