Conformal Invariants of Manifolds of Non-positive Scalar Curvature

Conformal invariants of manifolds of non-positive scalar curvature are studied in association with growth in volume and fundamental group.Comment: 12 pages, Latex Forma

Improving the Fidelity of Optical Zeno Gates via Distillation

We have modelled the Zeno effect Control-Sign gate of Franson et al (PRA 70, 062302, 2004) and shown that high two-photon to one-photon absorption ratios, $\kappa$, are needed for high fidelity free standing operation. Hence we instead employ this gate for cluster state fusion, where the requirement for $\kappa$ is less restrictive. With the help of partially offline one-photon and two-photon distillations, we can achieve a fusion gate with unity fidelity but non-unit probability of success. We conclude that for $\kappa > 2200$, the Zeno fusion gate will out perform the equivalent linear optics gate.Comment: 6 pages, 11 figures, Submitted to PR

Quantum Entanglement Capacity with Classical Feedback

For any quantum discrete memoryless channel, we define a quantity called quantum entanglement capacity with classical feedback ($E_B$), and we show that this quantity lies between two other well-studied quantities. These two quantities - namely the quantum capacity assisted by two-way classical communication ($Q_2$) and the quantum capacity with classical feedback ($Q_B$) - are widely conjectured to be different: there exists quantum discrete memoryless channel for which $Q_2>Q_B$. We then present a general scheme to convert any quantum error-correcting codes into adaptive protocols for this newly-defined quantity of the quantum depolarizing channel, and illustrate with Cat (repetition) code and Shor code. We contrast the present notion with entanglement purification protocols by showing that whilst the Leung-Shor protocol can be applied directly, recurrence methods need to be supplemented with other techniques but at the same time offer a way to improve the aforementioned Cat code. For the quantum depolarizing channel, we prove a formula that gives lower bounds on the quantum capacity with classical feedback from any $E_B$ protocols. We then apply this formula to the $E_B$ protocols that we discuss to obtain new lower bounds on the quantum capacity with classical feedback of the quantum depolarizing channel

A Walsh-Fourier approach to the circulant Hadamard conjecture

We describe an approach to the circulant Hadamard conjecture based on Walsh-Fourier analysis. We show that the existence of a circulant Hadamard matrix of order $n$ is equivalent to the existence of a non-trivial solution of a certain homogenous linear system of equations. Based on this system, a possible way of proving the conjecture is proposed.Comment: 8 page

A genetic-algorithms based evolutionary computational neural network for modelling spatial interaction data

Building a feedforward computational neural network model (CNN) involves two distinct tasks: determination of the network topology and weight estimation. The specification of a problem adequate network topology is a key issue and the primary focus of this contribution. Up to now, this issue has been either completely neglected in spatial application domains, or tackled by search heuristics (see Fischer and Gopal 1994). With the view of modelling interactions over geographic space, this paper considers this problem as a global optimization problem and proposes a novel approach that embeds backpropagation learning into the evolutionary paradigm of genetic algorithms. This is accomplished by interweaving a genetic search for finding an optimal CNN topology with gradient-based backpropagation learning for determining the network parameters. Thus, the model builder will be relieved of the burden of identifying appropriate CNN-topologies that will allow a problem to be solved with simple, but powerful learning mechanisms, such as backpropagation of gradient descent errors. The approach has been applied to the family of three inputs, single hidden layer, single output feedforward CNN models using interregional telecommunication traffic data for Austria, to illustrate its performance and to evaluate its robustness.