The six-vertex model on an N × N square lattice with domain wall boundary conditions is considered. A Fredholm determinant representation for the partition function of the model is given. The kernel of the corresponding integral operator is of the so-called integrable type, and involves classical orthogonal polynomials. From this representation, a " reconstruction " formula is proposed, which e...

A method is presented for the fast and accurate solution of elliptic boundary value problems on domains with corners. The method is based on integral equations and Nyström discretization. Close to corners two representations for the solution coexist – a pointwise representation and a representation in terms of special basis functions. Mappings and kernel evaluations are constructed on a symmetr...

Three types of HST: square tiling (e.g., Quadtree and Spatial Pyramid), rectangular tiling (HST-RECT), triangular tiling (HST-TRI) Representation Given a set of scene configurations (scene label maps), we present a learning-by-parsing (EM-like) method to learn the HST representation including the branching probability at Or-nodes and the tiling dictionary. E-Step: fix HST and infer parse tree b...

We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support an infinite tridiagonal matrix representation of the wave operator. The class of solutions obtained as such includes the discrete (for bound states) as well as the continuous (for scattering states) spectrum of the Hamiltonian. The problem translates into finding solution...

In this paper, we propose a new method for parameterizing a contractible domain (called the computational domain) which is defined by its boundary. Using a sequence of harmonic maps, we first build a mapping from the computational domain to the parameter domain, i.e., the unit square or unit cube. Then we parameterize the original domain by spline approximation of the inverse mapping. Numerical...

This paper is concerned with the construction of generalized Banach frames on homogeneous spaces. The major tool is a unitary group representation which is square integrable modulo a certain subgroup. By means of this representation, generalized coorbit spaces can be defined. Moreover, we can construct a specific reproducing kernel which, after a judicious discretization, gives rise to atomic d...

Scalar quantizers with the minimum mean square error are designed in the case where the input signal and the quantization noise are uncorrelated. The probability density function (pdf) of the stochastic signal is assumed to be known. This design is then generalized to vector quantizers in the case where the expected value of the inner product between the input and quantization noise vector are ...

Advanced geospatial applications often involve complex computing operations performed under sometimes severe resource constraints. These applications primarily rely on traditional raster and vector data structures based on square lattices. But there is a significant body of research that indicates that data structures based on hexagonal lattices may be a superior alternative for efficient repre...