This paper presents a method to compute the quasi-conformal parameterization (QCMC) for a multiply-connected 2D domain or surface. QCMC computes a quasi-conformal map from a multiply-connected domain S onto a punctured disk DS associated with a given Beltrami differential. The Beltrami differential, which measures the conformality distortion, is a complexvalued function μ : S → C with supremum ...

In this work we develop a dynamically adaptive sparse grids (SG) method for quasi-optimal interpolation of multidimensional analytic functions defined over a product of one dimensional bounded domains. The goal of such approach is to construct an interpolant in space that corresponds to the “best M -terms” based on sharp a priori estimate of polynomial coefficients. In the past, SG methods have...

The least squares problem is formulated in terms of lp quasi-norm regularization (0 < p < 1). Two formulations are considered: (i) an lp-constrained optimization and (ii) an lp-penalized (unconstrained) optimization. Due to the nonconvexity of the lp quasi-norm, the solution paths of the regularized least squares problem are not ensured to be continuous. A critical path, which is a maximal cont...

In this supplementary material, we give the detailed proofs of some lemmas, properties and theorems, as well as some additional experimental results on synthetic data and four recommendation system data sets. A More Notations R n denotes the n-dimensional Euclidean space, and the set of all m×n matrices with real entries is denoted by R m×n. Given matrices X and Y ∈ R m×n , the inner product is...

We present a DOA estimation algorithm, called Joint-Sparse DOA to address the problem of direction-of-arrival (DOA) estimation using sensor arrays. Firstly, DOA estimation is cast as the joint-sparse recovery problem. Then, norm is approximated by an arctan function to represent joint sparsity and DOA estimation can be obtained by minimizing the approximate norm. Finally, the minimization probl...

Tensor rank and low-rank tensor decompositions have many applications in learning and complexity theory. Most known algorithms use unfoldings of tensors and can only handle rank up to nbp/2c for a p-th order tensor in Rnp . Previously no efficient algorithm can decompose 3rd order tensors when the rank is super-linear in the dimension. Using ideas from sum-of-squares hierarchy, we give the firs...

background : since risk factors of hypertension are formed during adolescent period and regarding that attitudes change occurs more easily in these ages, the present paper aimed to evaluate the impact of education based on the theory of planned behavior in hypertension prevention behaviors in female adolescent students. methods : in this quasi-experimental study, 160 girls of 12-16 yr old (80 i...

We study eigenfunctions φj and eigenvalues Ej of the Dirichlet Laplacian on a bounded domain Ω ⊂ Rn with piecewise smooth boundary. We bound the distance between an arbitrary parameter E > 0 and the spectrum {Ej} in terms of the boundary L2-norm of a normalized trial solution u of the Helmholtz equation (∆ + E)u = 0. We also bound the L2-norm of the error of this trial solution from an eigenfun...