An iterative scheme for constructing compactly supported orthonormal (o.n.) multi-wavelets with vanishing moments of arbitrarily high order is established. Precisely, let φ = [φ1, · · · , φr] be an r-dimensional o.n. scaling function vector with polynomial preservation of order (p.p.o.) m, and ψ = [ψ1, · · · , ψr] an o.n. multiwavelet corresponding to φ, with two-scale symbols P and Q, respecti...

A recently introduced method for determining the critical indices of the deconfinement transition in gauge theories, already tested for the case of 3D SU(3) pure gauge theory, is applied here to 4D SU(2) pure gauge theory. The method is inspired by universality and based on the finite size scaling behavior of the expectation value of simple lattice operators, such as the plaquette. We obtain an...

An estimate is given for the support of each component function of a compactly supported scaling vector satisfying a matrix refinement equation with finite number of terms. The estimate is based on the highest and lowest degree of each polynomial in the corresponding matrix symbol. Only basic techniques from matrix theory are involved in the derivation.

For combining classifiers at measurement level, the diverse outputs of classifiers should be transformed to uniform measures that represent the confidence of decision, hopefully, the class probability or likelihood. This paper presents our experimental results of classifier combination using confidence evaluation. We test three types of confidences: log-likelihood, exponential and sigmoid. For ...

A new adaptation scheme for adapting arbitrary normal mutation distributions in evolution strategies is introduced. It can adapt correct scaling and correlations between object parameters. Furthermore, it is independent of any rotation of the objective function and reliably adapts mutation distributions corresponding to hyperellipsoids with high axis ratio. In simulations, the generating set ad...

Moreover, if p , q, then the inequality is strict. A proof: The map u 7→ −u log u is strictly concave on [0, 1]; this follows from the fact that its derivative −(1 + log u) is strictly decreasing on [0, 1]. Now, a sum of concave functions is concave, so we conclude that H is concave. Moreover, if p , q, then they differ in some coordinate; strict concavity of the map u 7→ −u log u applied to th...

We construct new algorithms from scratch, which use the fourth order cumulant of stochastic variables for the cost function. The multiplicative updating rule here constructed is natural from the homogeneous nature of the Lie group and has numerous merits for the rigorous treatment of the dynamics. As one consequence, the second order convergence is shown. For the cost function, functions invari...

We present a novel image resizing method which attempts to ensure that important local regions undergo a geometric similarity transformation, and at the same time, to preserve image edge structure. To accomplish this, we define handles to describe both local regions and image edges, and assign a weight for each handle based on an importance map for the source image. Inspired by conformal energy...

We propose a new form for equations of state (EOS) of thermodynamic systems in the Ising universality class. The new EOS guarantees the correct universality and scaling behavior close to critical points and is formulated in terms of the scaling fields only – unlike the traditional Schofield representation, which uses a parametric form. Close to a critical point, the new EOS expresses the square...

We apply the Lax-Phillips wave equation scattering theory to multiresolutions associated with wavelets: For the wavelet scattering, the translation symmetry, the scaling operator, and the scaling function are identiied in the scattering theoretic spectral transform; the scaling function is shown to be analytic; and an analytic spectral function is identiied as an invariant for multiresolutions,...