A Hybrid Reasoning Model for “Whole and Part” Cardinal Direction Relations

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 our previous papers (Kor and Bennett, 2003 and 2010). 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 basic binary relations and 13 feasible as well as jointly exhaustive relations for the x- and y-directions, respectively. Based on these basic binary relations, we derive two separate 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

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

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 Ontology for Grounding Vague Geographic Terms

Many geographic terms, such as “river” and “lake”, are vague, with no clear boundaries of application. In particular, the spatial extent of such features is often vaguely carved out of a continuously varying observable domain. We present a means of defining vague terms using standpoint semantics, a refinement of the philosophical idea of supervaluation semantics. Such definitions can be grounded in actual data by geometric analysis and segmentation of the data set. The issues raised by this process with regard to the nature of boundaries and domains of logical quantification are discussed. We describe a prototype implementation of a system capable of segmenting attributed polygon data into geographically significant regions and evaluating queries involving vague geographic feature terms

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

Enabling Data-Driven Transportation Safety Improvements in Rural Alaska

Safety improvements require funding. A clear need must be demonstrated to secure funding. For transportation safety, data, especially data about past crashes, is the usual method of demonstrating need. However, in rural locations, such data is often not available, or is not in a form amenable to use in funding applications. This research aids rural entities, often federally recognized tribes and small villages acquire data needed for funding applications. Two aspects of work product are the development of a traffic counting application for an iPad or similar device, and a review of the data requirements of the major transportation funding agencies. The traffic-counting app, UAF Traffic, demonstrated its ability to count traffic and turning movements for cars and trucks, as well as ATVs, snow machines, pedestrians, bicycles, and dog sleds. The review of the major agencies demonstrated that all the likely funders would accept qualitative data and Road Safety Audits. However, quantitative data, if it was available, was helpful

A Closed-Form Expression for the Gravitational Radiation Rate from Cosmic Strings

We present a new formula for the rate at which cosmic strings lose energy into gravitational radiation, valid for all piecewise-linear cosmic string loops. At any time, such a loop is composed of $N$ straight segments, each of which has constant velocity. Any cosmic string loop can be arbitrarily-well approximated by a piecewise-linear loop with $N$ sufficiently large. The formula is a sum of $O(N^4)$ polynomial and log terms, and is exact when the effects of gravitational back-reaction are neglected. For a given loop, the large number of terms makes evaluation ``by hand" impractical, but a computer or symbolic manipulator yields accurate results. The formula is more accurate and convenient than previous methods for finding the gravitational radiation rate, which require numerical evaluation of a four-dimensional integral for each term in an infinite sum. It also avoids the need to estimate the contribution from the tail of the infinite sum. The formula has been tested against all previously published radiation rates for different loop configurations. In the cases where discrepancies were found, they were due to errors in the published work. We have isolated and corrected both the analytic and numerical errors in these cases. To assist future work in this area, a small catalog of results for some simple loop shapes is provided.Comment: 29 pages TeX, 16 figures and computer C-code available via anonymous ftp from directory pub/pcasper at alpha1.csd.uwm.edu, WISC-MILW-94-TH-10, (section 7 has been expanded, two figures added, and minor grammatical changes made.

Remote State Preparation

Quantum teleportation uses prior entanglement and forward classical communication to transmit one instance of an unknown quantum state. Remote state preparation (RSP) has the same goal, but the sender knows classically what state is to be transmitted. We show that the asymptotic classical communication cost of RSP is one bit per qubit - half that of teleportation - and becomes even less when transmitting part of a known entangled state. We explore the tradeoff between entanglement and classical communication required for RSP, and discuss RSP capacities of general quantum channels.Comment: 4 pages including 1 epsf figure; v3 has an additional author and discusses relation to work of Devetak and Berger (quant-ph/0102123); v4 improves low-entanglement protocols without back communication to perform as well as low-entanglement protocols with back communication; v5 (journal version) has a few small change

Nonorthogonal Quantum States Maximize Classical Information Capacity

I demonstrate that, rather unexpectedly, there exist noisy quantum channels for which the optimal classical information transmission rate is achieved only by signaling alphabets consisting of nonorthogonal quantum states.Comment: 5 pages, REVTeX, mild extension of results, much improved presentation, to appear in Physical Review Letter

Quantum cryptography with squeezed states

A quantum key distribution scheme based on the use of displaced squeezed vacuum states is presented. The states are squeezed in one of two field quadrature components, and the value of the squeezed component is used to encode a character from an alphabet. The uncertainty relation between quadrature components prevents an eavesdropper from determining both with enough precision to determine the character being sent. Losses degrade the performance of this scheme, but it is possible to use phase-sensitive amplifiers to boost the signal and partially compensate for their effect.Comment: 15 pages, no figure