This paper presents a novel image representation, which incorporates the principles of Laplacian Pyramid into the irregular graph pyramid. The drawback of the regular Laplacian Pyramid is their lack to keep the topological structure of the image, due to the contraction process in building the Gaussian Pyramid. Irregular graph pyramid is able to hierarchically represent the topological structure...

Motivated by a recent paper of Louko and Molgado, we consider a simple system with a single classical constraint R(q) = 0. If ql denotes a generic solution to R(q) = 0, our examples include cases where R(ql) 6= 0 (regular constraint) and R(ql) = 0 (irregular constraint) of varying order as well as the case where R(q) = 0 for an interval, such as a ≤ q ≤ b. Quantization of irregular constraints ...

The irregularity of a graph G is defined as irr(G) = ∑ |d(x) − d(y)| where d(x) is the degree of vertex x and the summation embraces all pairs of adjacent vertices of G. We characterize the graphs minimum and maximum values of irr.

We present extensions of the classical Poisson summation formula in which the sequence of sampling knots, normally a lattice, can be taken from a relatively wide class of sequences.

We present a generalization of the commutation formula to irregular subdivision schemes and wavelets. We show how, in the noninterpolating case, the divided differences need to be adapted to the subdivision scheme. As an example we include the construction of an entire family of biorthogonal compactly supported irregular knot B-spline wavelets starting from Lagrangian interpolation.

Simple answers are given to the following and related questions: For what Hubert space operator A is it true that the smallest ideal (alternatively, the smallest norm ideal, the smallest maximal norm ideal) containing A is a norm (an intermediate norm, a principal norm) ideal? Do these ideals support a nontrivial unitary invariant positive linear functional?

Software developers for distributed memory multiprocessors often complain about the lack of libraries and tools for developing and performance tuning their applications. While some tools exist for regular array-based computations , support for applications with pointer-based data structures, asyn-chronous communication patterns, or unpredictable computational costs is seriously lacking. In this...

FACULTY OF ENGINEERING, SCIENCE AND MATHEMATICS SCHOOL OF ELECTRONICS AND COMPUTER SCIENCE Doctor of Philosophy Irregular Variable Length Coding by Robert G. Maunder In this thesis, we introduce Irregular Variable Length Coding (IrVLC) and investigate its applications, characteristics and performance in the context of digital multimedia broadcast telecommunications. During IrVLC encoding, the m...

The new prooles of the space missions aimed at asteroids and comets, moving from y{bys to rendez{ vous and orbiting, call for new spaceeight dynamics tools capable of propagating orbits in an accurate way around these small irregular objects. Moreover, interesting celestial mechanics and planetary science problems, requiring the same sophisticated tools, have been raised by the rst images of as...

A graph G is locally irregular if adjacent vertices of G have distinct degrees. An edge colouring of G is locally irregular if each of its colours induces a locally irregular subgraph of G. The irregular chromatic index of G refers to the least number of colours used by a locally irregular edge colouring of G (if any). We propose a linear-time algorithm for determining the irregular chromatic i...