We consider the question whether all the coefficients in the series expansions of some specific rational functions are positive, and we demonstrate how computer algebra can help answering questions arising in this context. By giving partial computer proofs, we provide new evidence in support of some longstanding open conjectures. Also two new conjectures are made.

Increase of digital storage capacity enabled the creation of large-scale news video archives. To make full use of the archive, it is necessary to grasp the development and dependencies of news stories. Considering this problem, we investigate tracking and re-ranking methodologies of news stories. The archive used as a test-bed consists of more than 30,000 news stories. This paper proposes a nov...

The paper presents the abstraction transformation which is a fundamental method for creating functions in ADATE. The use of abstraction turns out to be similar to evolution by gene duplication which is emerging as the most important theory of \building blocks" in natural genomes. We discuss the relationship between abstraction and its natural counterparts, but also give novel technical details ...

Considerable work has been devoted to the question of how best to parameterize the properties of dark energy, in particular its equation of state w. We argue that, in the absence of a compelling model for dark energy, the parameterizations of functions about which we have no prior knowledge, such as w(z), should be determined by the data rather than by our ingrained beliefs or familiar series e...

We present a novel surface smoothing framework using the Laplace-Beltrami eigenfunctions. The Green’s function of an isotropic diffusion equation on a manifold is analytically represented using the eigenfunctions of the Laplace-Beltraimi operator. The Green’s function is then used in explicitly constructing heat kernel smoothing as a series expansion of the eigenfunctions. Unlike many previous ...

We demonstrate a specific power series expansion technique to solve the three-dimensional homogeneous and inhomogeneous wave equations. As solving functions, so-called wave polynomials are used. The presented method is useful for a finite body of certain shape. Recurrent formulas to improve efficiency are obtained for the wave polynomials and their derivatives in a Cartesian, spherical, and cyl...

A feature of certain ensembles of random matrices is that the corresponding measure is invariant under conjugation by unitary matrices. Study of such ensembles realised by matrices with Gaussian entries leads to statistical quantities related to the eigenspectrum, such as the distribution of the largest eigenvalue, which can be expressed as multidimensional integrals or equivalently as determin...

The subjective tests used to evaluate image and video quality estimators (QEs) are expensive and time consuming. More problematic, the majority of subjective testing is not designed to find systematic weaknesses in the evaluated QEs. As a result, a motivated attacker can take advantage of these systematic weaknesses to gain unfair monetary advantage. In this paper, we draw on some lessons of so...

In this paper we give some background theory on the concept of fractional calculus, in particular the Riemann-Liouville operators. We then investigate the Taylor-Riemann series using Osler’s theorem and obtain certain double infinite series expansions of some elementary functions. In the process of this we give a proof of the convergence of an alternative form of Heaviside’s series. A Semi-Tayl...

In information retrieval, queries can fail to find documents due to mismatch in terminology. Query expansion is a well-known technique addressing this problem, where additional query terms are automatically chosen from highly ranked documents, and it has been shown to be effective at improving query performance. However, current techniques for query expansion use fixed values for key parameters...