Embedding partial G-designs where G is a 4-cycle with a pendant edge

Let D denote the graph consisting of a cycle of length 4 with a pendant edge. In this paper, two very different small embeddings of partial D-designs are presented. (c) 2005 Elsevier B.V. All rights reserved.

Embedding a restricted class of partial K-4-designs

Given a partial K-4-design (X, P), if x is an element of X is a vertex which occurs in exactly one block of P, then call x a free vertex. In this paper, a technique is described for obtaining a cubic embedding of any partial K-4-design with the property that every block in the partial design contains at least two free vertices.

Embedding defeasible logic into logic programming

Defeasible reasoning is a simple but efficient approach to nonmonotonic reasoning that has recently attracted considerable interest and that has found various applications. Defeasible logic and its variants are an important family of defeasible reasoning methods. So far no relationship has been established between defeasible logic and mainstream nonmonotonic reasoning approaches. In this paper we establish close links to known semantics of logic programs. In particular, we give a translation of a defeasible theory D into a meta-program P(D). We show that under a condition of decisiveness, the defeasible consequences of D correspond exactly to the sceptical conclusions of P(D) under the stable model semantics. Without decisiveness, the result holds only in one direction (all defeasible consequences of D are included in all stable models of P(D)). If we wish a complete embedding for the general case, we need to use the Kunen semantics of P(D), instead.

Existence and embeddings of partial Steiner triple systems of order ten with cubic leaves

Denote the set of 21 non-isomorphic cubic graphs of order 10 by L. We first determine precisely which L is an element of L occur as the leave of a partial Steiner triple system, thus settling the existence problem for partial Steiner triple systems of order 10 with cubic leaves. Then we settle the embedding problem for partial Steiner triple systems with leaves L is an element of L. This second result is obtained as a corollary of a more general result which gives, for each integer v greater than or equal to 10 and each L is an element of L, necessary and sufficient conditions for the existence of a partial Steiner triple system of order v with leave consisting of the complement of L and v - 10 isolated vertices. (C) 2004 Elsevier B.V. All rights reserved.

Embeddings of partial Steiner triple systems

Any partial Steiner triple system of order u can be embedded in a Steiner triple system of order v if v equivalent to 1, 3 (mod 6) and v greater than or equal to 3u - 2. (C) 2004 Elsevier Inc. All rights reserved.

Quantum trajectories for the realistic measurement of a solid-state charge qubit

We present a new model for the continuous measurement of a coupled quantum dot charge qubit. We model the effects of a realistic measurement, namely adding noise to, and filtering, the current through the detector. This is achieved by embedding the detector in an equivalent circuit for measurement. Our aim is to describe the evolution of the qubit state conditioned on the macroscopic output of the external circuit. We achieve this by generalizing a recently developed quantum trajectory theory for realistic photodetectors [P. Warszawski, H. M. Wiseman, and H. Mabuchi, Phys. Rev. A 65, 023802 (2002)] to treat solid-state detectors. This yields stochastic equations whose (numerical) solutions are the realistic quantum trajectories of the conditioned qubit state. We derive our general theory in the context of a low transparency quantum point contact. Areas of application for our theory and its relation to previous work are discussed.

Sharp Sobolev inequality involving a critical nonlinearity on a boundary

We consider the solvability of the Neumann problem for the equation -Delta u + lambda u = 0, partial derivative u/partial derivative v = Q(x)vertical bar u vertical bar(q-2)u on partial derivative Omega, where Q is a positive and continuous coefficient on partial derivative Omega, lambda is a parameter and q = 2(N - 1)/(N - 2) is a critical Sobolev exponent for the trace embedding of H-1(Omega) into L-q(partial derivative Omega). We investigate the joint effect of the mean curvature of partial derivative Omega and the shape of the graph of Q on the existence of solutions. As a by product we establish a sharp Sobolev inequality for the trace embedding. In Section 6 we establish the existence of solutions when a parameter lambda interferes with the spectrum of -Delta with the Neumann boundary conditions. We apply a min-max principle based on the topological linking.

3D statistical shape models to embed spatial relationship information

This paper presents the creation of 3D statistical shape models of the knee bones and their use to embed information into a segmentation system for MRIs of the knee. We propose utilising the strong spatial relationship between the cartilages and the bones in the knee by embedding this information into the created models. This information can then be used to automate the initialisation of segmentation algorithms for the cartilages. The approach used to automatically generate the 3D statistical shape models of the bones is based on the point distribution model optimisation framework of Davies. Our implementation of this scheme uses a parameterized surface extraction algorithm, which is used as the basis for the optimisation scheme that automatically creates the 3D statistical shape models. The current approach is illustrated by generating 3D statistical shape models of the patella, tibia and femoral bones from a segmented database of the knee. The use of these models to embed spatial relationship information to aid in the automation of segmentation algorithms for the cartilages is then illustrated.

A partial-correctness semantics for modelling assembler programs

Previous work on formally modelling and analysing program compilation has shown the need for a simple and expressive semantics for assembler level programs. Assembler programs contain unstructured jumps and previous formalisms have modelled these by using continuations, or by embedding the program in an explicit emulator. We propose a simpler approach, which uses techniques from compiler theory in a formal setting. This approach is based on an interpretation of programs as collections of program paths, each of which has a weakest liberal precondition semantics. We then demonstrate, by example, how we can use this formalism to justify the compilation of block-structured high-level language programs into assembler.