Composition for cardinal directions by decomposing horizontal and vertical constraints

In this paper, we demonstrate how to group the nine cardinal directions into sets and use them to compute a composition table. Firstly, we define each cardinal direction in terms of a certain set of constraints. This is followed by decomposing the cardinal directions into sets corresponding to the horizontal and vertical constraints. We apply two different techniques to compute the composition of these sets. The first technique is an algebraic computation while the second is the typical technique of reasoning with diagrams. The rationale of applying the latter is for confirmation purposes. The use of typical composition tables for existential inference is rarely demonstrated. Here, we shall demonstrate how to use the composition table to answer queries requiring the common forward reasoning as well as existential inference. Also, we combine mereological and cardinal direction relations to create a hybrid model which is more expressive

An expressive hybrid model for the composition of cardinal directions

In our previous paper (Kor and Bennett, 2003), we have shown how the nine tiles in the projection-based model for cardinal directions can be partitioned into sets based on horizontal and vertical constraints (called Horizontal and Vertical Constraints Model). In order to come up with an expressive hybrid model for direction relations between two-dimensional single-piece regions (without holes), we integrate the well-known RCC-8 model with the above-mentioned model. From this expressive hybrid model, we derive 8 atomic binary relations and 13 feasible as well as jointly exhaustive relations for the x and y directions respectively. Based on these atomic binary relations, we derive two separate 8x8 composition tables for both the expressive and weak direction relations. We introduce a formula that can be used for the computation of the composition of expressive and weak direction relations between ‘whole or part’ regions. Lastly, we also show how the expressive hybrid model can be used to make several existential inferences that are not possible for existing models

Full counting statistics and conditional evolution in a nanoelectromechanical system

We study theoretically the full distribution of transferred charge in a tunnel junction (or quantum point contact) coupled to a nanomechanical oscillator, as well as the conditional evolution of the oscillator. Even if the oscillator is very weakly coupled to the tunnel junction, it can strongly affect the tunneling statistics and lead to a highly non-Gaussian distribution. Conversely, given a particular measurement history of the current, the oscillator energy distribution may be localized and highly non-thermal. We also discuss non-Gaussian correlations between the oscillator motion and tunneling electrons; these show that the tunneling back-action cannot be fully described as an effective thermal bath coupled to the oscillator.Comment: 7 pages; figure added; typos correcte

The Power of LOCCq State Transformations

Reversible state transformations under entanglement non-increasing operations give rise to entanglement measures. It is well known that asymptotic local operations and classical communication (LOCC) are required to get a simple operational measure of bipartite pure state entanglement. For bipartite mixed states and multipartite pure states it is likely that a more powerful class of operations will be needed. To this end \cite{BPRST01} have defined more powerful versions of state transformations (or reducibilities), namely LOCCq (asymptotic LOCC with a sublinear amount of quantum communication) and CLOCC (asymptotic LOCC with catalysis). In this paper we show that {\em LOCCq state transformations are only as powerful as asymptotic LOCC state transformations} for multipartite pure states. We first generalize the concept of entanglement gambling from two parties to multiple parties: any pure multipartite entangled state can be transformed to an EPR pair shared by some pair of parties and that any irreducible $m$ $(m\ge 2)$ party pure state can be used to create any other state (pure or mixed), using only local operations and classical communication (LOCC). We then use this tool to prove the result. We mention some applications of multipartite entanglement gambling to multipartite distillability and to characterizations of multipartite minimal entanglement generating sets. Finally we discuss generalizations of this result to mixed states by defining the class of {\em cat distillable states}

Solving surface structures from normal incidence X-ray standing wave data

A program is provided to determine structural parameters of atoms in or adsorbed on surfaces by refinement of atomistic models towards experimentally determined data generated by the normal incidence X-ray standing wave (NIXSW) technique. The method employs a combination of Differential Evolution Genetic Algorithms and Steepest Descent Line Minimisations to provide a fast, reliable and user friendly tool for experimentalists to interpret complex multidimensional NIXSW data sets

Review of river fisheries valuation in Central and South America

Unlike Africa and Asia, where a large part of the population are heavily dependent upon fishing for their livelihoods, fishing for a living in the interior of Central and South America (CSA) remains a marginal occupation for all but the most isolated of families. As such, the economics and management of fisheries on the continent have received little attention from within the continent and the rest of the world. This study shows that while a number of studies have been carried out on fishing in the region, they tend to be limited in their geographical focus and time scale. Although fishing of freshwater species may appear to be comparatively insignificant in the region, the rivers of CSA are very important. This report attempts to analyze the literature available on CSA river fisheries and attempts to draw out an economic value of these fisheries. It is divided into a number of sections. First, the authors describe the major river basins on the continent, characterize their fisheries, and place freshwater fisheries in CSA into a global context. Second, the authors provide a review of valuation techniques for fisheries and use this analytical framework to review the principal literature on freshwater fisheries in the region. Then they turn their attention to the economic impact of dams and water abstraction schemes, reviewing the available literature to ascertain how/if economic values are computed for the impact on fisheries. Finally, they offer some conclusions and recommendations on the direction for future studies of freshwater fisheries in CSA

The Parity Bit in Quantum Cryptography

An $n$-bit string is encoded as a sequence of non-orthogonal quantum states. The parity bit of that $n$-bit string is described by one of two density matrices, $\rho_0^{(n)}$ and $\rho_1^{(n)}$, both in a Hilbert space of dimension $2^n$. In order to derive the parity bit the receiver must distinguish between the two density matrices, e.g., in terms of optimal mutual information. In this paper we find the measurement which provides the optimal mutual information about the parity bit and calculate that information. We prove that this information decreases exponentially with the length of the string in the case where the single bit states are almost fully overlapping. We believe this result will be useful in proving the ultimate security of quantum crytography in the presence of noise.Comment: 19 pages, RevTe