This paper considers Gibbs’ phenomenon for scaling vectors in L2(R). We first show that a wide class of multiresolution analyses suffer from Gibbs’ phenomenon. To deal with this problem, in [11], Walter and Shen use an Abel summation technique to construct a positive scaling function Pr, 0 < r < 1, from an orthonormal scaling function φ that generates V0. A reproducing kernel can in turn be con...

We introduce a novel graph kernel called the Neighborhood Subgraph Pairwise Distance Kernel. The kernel decomposes a graph into all pairs of neighborhood subgraphs of small radius at increasing distances. We show that using a fast graph invariant we obtain significant speed-ups in the Gram matrix computation. Finally, we test the novel kernel on a wide range of chemoinformatics tasks, from anti...

Once one has these two properties, one obtains several additional properties for free, such as boundedness on L(R) for all 1 < p < ∞; also T and T ∗ both map L to BMO. However, it is not always easy to verify these properties in practice. The singular kernel properties are usually not too difficult, as the kernel can often be expressed directly, and then estimated pointwise in a fairly straight...

In [14], Walter and Shen use an Abel summation technique to construct a positive scaling function Pr, 0 < r < 1, from an orthonormal scaling function φ that generates V0. A reproducing kernel can in turn be constructed using Pr. This kernel is also positive, has unit integral, and approximations utilitizing it display no Gibbs’ phenomenon. These results were extended to scaling vectors and mult...

We propose a semiparametric approach for testing orthogonality and causality between two infiniteorder cointegrated vector autoregressive IVAR(1) series. The procedures considered can be viewed as extensions of classical methods proposed by Haugh (1976, JASA) and Hong (1996, Biometrika) for testing independence between stationary univariate time series. The tests are based on the residuals of l...

We show that limit transitions from Askey-Wilson polynomials to q-Racah, little and big q-Jacobi polynomials can be made rigorous on the level of their orthogonality measures in a suitable weak sense. This allows us to derive the orthogonality relations and norm evaluations for the q-Racah polynomials, little and big q-Jacobi polynomials by taking limits in the orthogonality relations and norm ...

In this paper, we derive upper bounds for the heat kernel of the simple random walk on the infinite cluster of a supercritical long range percolation process. For any d ≥ 1 and for any exponent s ∈ (d, (d + 2) ∧ 2d) giving the rate of decay of the percolation process, we show that the return probability decays like t− /s−d up to logarithmic corrections, where t denotes the time the walk is run....