Performance of a New Enhanced Topological Decision-Rule Map-Matching Algorithm for Transportation Applications

Indexación: Web of Science; ScieloMap-matching problems arise in numerous transportation-related applications when spatial data is collected using inaccurate GPS technology and integrated with a flawed digital roadway map in a GIS environment. This paper presents a new enhanced post-processing topological decision-rule map-matching algorithm in order to address relevant special cases that occur in the spatial mismatch resolution. The proposed map-matching algorithm includes simple algorithmic improvements: dynamic buffer that varies its size to snap GPS data points to at least one roadway centerline; a comparison between vehicle heading measurements and associated roadway centerline direction; and a new design of the sequence of steps in the algorithm architecture. The original and new versions of the algorithm were tested on different spatial data qualities collected in Canada and United States. Although both versions satisfactorily resolve complex spatial ambiguities, the comparative and statistical analysis indicates that the new algorithm with the simple algorithmic improvements outperformed the original version of the map-matching algorithm.El problema de la ambigüedad espacial ocurre en varias aplicaciones relacionadas con transporte, específicamente cuando existe inexactitud en los datos espaciales capturados con tecnología GPS o cuando son integrados con un mapa digital que posee errores en un ambiente SIG. Este artículo presenta un algoritmo nuevo y mejorado basado en reglas de decisión que es capaz de resolver casos especiales relevantes en modo post-proceso. El algoritmo propuesto incluye las siguientes mejoras algorítmicas: un área de búsqueda dinámica que varía su tamaño para asociar puntos GPS a al menos un eje de calzada, una comparación entre el rumbo del vehículo y la dirección del eje de calzada asignada, y un nuevo diseño de la secuencia de pasos del algoritmo. Tanto el algoritmo original como el propuesto fueron examinados con datos espaciales de diferentes calidades capturados en Canadá y Estados Unidos. Aunque ambas versiones resuelven satisfactoriamente el problema de ambigüedad espacial, el análisis comparativo y estadístico indica que la nueva versión del algoritmo con las mejoras algorítmicas entrega resultados superiores a la versión original del algoritmo.http://ref.scielo.org/9mt55

Brane world solutions of perfect fluid in the background of a bulk containing dust or cosmological constant

The paper presents some solutions to the five dimensional Einstein equations due to a perfect fluid on the brane with pure dust filling the entire bulk in one case and a cosmological constant (or vacuum) in the bulk for the second case. In the first case, there is a linear relationship between isotropic pressure, energy density and the brane tension, while in the second case, the perfect fluid is assumed to be in the form of chaplygin gas. Cosmological solutions are found both for brane and bulk scenarios and some interesting features are obtained for the chaplygin gas on the brane which are distinctly different from the standard cosmology in four dimensions.Comment: 10 Latex pages, 5 figure

Exterior spacetime for stellar models in 5-dimensional Kaluza-Klein gravity

It is well-known that Birkhoff's theorem is no longer valid in theories with more than four dimensions. Thus, in these theories the effective 4-dimensional picture allows the existence of different possible, non-Schwarzschild, scenarios for the description of the spacetime outside of a spherical star, contrary to general relativity in 4D. We investigate the exterior spacetime of a spherically symmetric star in the context of Kaluza-Klein gravity. We take a well-known family of static spherically symmetric solutions of the Einstein equations in an empty five-dimensional universe, and analyze possible stellar exteriors that are conformal to the metric induced on four-dimensional hypersurfaces orthogonal to the extra dimension. All these exteriors are continuously matched with the interior of the star. Then, without making any assumptions about the interior solution, we prove the following statement: the condition that in the weak-field limit we recover the usual Newtonian physics singles out an unique exterior. This exterior is "similar" to Scharzschild vacuum in the sense that it has no effect on gravitational interactions. However, it is more realistic because instead of being absolutely empty, it is consistent with the existence of quantum zero-point fields. We also examine the question of how would the deviation from the Schwarzschild vacuum exterior affect the parameters of a neutron star. In the context of a model star of uniform density, we show that the general relativity upper limit M/R < 4/9 is significantly increased as we go away from the Schwarzschild vacuum exterior. We find that, in principle, the compactness limit of a star can be larger than 1/2, without being a black hole. The generality of our approach is also discussed.Comment: Typos corrected. Accepted for publication in Classical and Quantum Gravit

Wave-like Solutions for Bianchi type-I cosmologies in 5D

We derive exact solutions to the vacuum Einstein field equations in 5D, under the assumption that (i) the line element in 5D possesses self-similar symmetry, in the classical understanding of Sedov, Taub and Zeldovich, and that (ii) the metric tensor is diagonal and independent of the coordinates for ordinary 3D space. These assumptions lead to three different types of self-similarity in 5D: homothetic, conformal and "wave-like". In this work we present the most general wave-like solutions to the 5D field equations. Using the standard technique based on Campbell's theorem, they generate a large number of anisotropic cosmological models of Bianchi type-I, which can be applied to our universe after the big-bang, when anisotropies could have played an important role. We present a complete review of all possible cases of self-similar anisotropic cosmologies in 5D. Our analysis extends a number of previous studies on wave-like solutions in 5D with spatial spherical symmetry

Hydrostatic Equilibrium of a Perfect Fluid Sphere with Exterior Higher-Dimensional Schwarzschild Spacetime

We discuss the question of how the number of dimensions of space and time can influence the equilibrium configurations of stars. We find that dimensionality does increase the effect of mass but not the contribution of the pressure, which is the same in any dimension. In the presence of a (positive) cosmological constant the condition of hydrostatic equilibrium imposes a lower limit on mass and matter density. We show how this limit depends on the number of dimensions and suggest that $\Lambda > 0$ is more effective in 4D than in higher dimensions. We obtain a general limit for the degree of compactification (gravitational potential on the boundary) of perfect fluid stars in $D$-dimensions. We argue that the effects of gravity are stronger in 4D than in any other number of dimensions. The generality of the results is also discussed

An analytic model for the transition from decelerated to accelerated cosmic expansion

We consider the scenario where our observable universe is devised as a dynamical four-dimensional hypersurface embedded in a five-dimensional bulk spacetime, with a large extra dimension, which is the {\it generalization of the flat FRW cosmological metric to five dimensions}. This scenario generates a simple analytical model where different stages of the evolution of the universe are approximated by distinct parameterizations of the {\it same} spacetime. In this model the evolution from decelerated to accelerated expansion can be interpreted as a "first-order" phase transition between two successive stages. The dominant energy condition allows different parts of the universe to evolve, from deceleration to acceleration, at different redshifts within a narrow era. This picture corresponds to the creation of bubbles of new phase, in the middle of the old one, typical of first-order phase transitions. Taking $\Omega_{m} = 0.3$ today, we find that the cross-over from deceleration to acceleration occurs at $z \sim 1-1.5$, regardless of the equation of state in the very early universe. In the case of primordial radiation, the model predicts that the deceleration parameter "jumps" from $q \sim + 1.5$ to $q \sim - 0.4$ at $z \sim 1.17$. At the present time $q = - 0.55$ and the equation of state of the universe is $w = p/\rho \sim - 0.7$, in agreement with observations and some theoretical predictions.Comment: The abstract and introduction are improved and the discussion section is expanded. A number of references are adde

Mass and Charge in Brane-World and Non-Compact Kaluza-Klein Theories in 5 Dim

In classical Kaluza-Klein theory, with compactified extra dimensions and without scalar field, the rest mass as well as the electric charge of test particles are constants of motion. We show that in the case of a large extra dimension this is no longer so. We propose the Hamilton-Jacobi formalism, instead of the geodesic equation, for the study of test particles moving in a five-dimensional background metric. This formalism has a number of advantages: (i) it provides a clear and invariant definition of rest mass, without the ambiguities associated with the choice of the parameters used along the motion in 5D and 4D, (ii) the electromagnetic field can be easily incorporated in the discussion, and (iii) we avoid the difficulties associated with the "splitting" of the geodesic equation. For particles moving in a general 5D metric, we show how the effective rest mass, as measured by an observer in 4D, varies as a consequence of the large extra dimension. Also, the fifth component of the momentum changes along the motion. This component can be identified with the electric charge of test particles. With this interpretation, both the rest mass and the charge vary along the trajectory. The constant of motion is now a combination of these quantities. We study the cosmological variations of charge and rest mass in a five-dimensional bulk metric which is used to embed the standard k = 0 FRW universes. The time variations in the fine structure "constant" and the Thomson cross section are also discussed.Comment: V2: References added, discussion extended. V3 is identical to V2, references updated. To appear in General Relativity and Gravitatio

Equivalence Between Space-Time-Matter and Brane-World Theories

We study the relationship between space-time-matter (STM) and brane theories. These two theories look very different at first sight, and have different motivation for the introduction of a large extra dimension. However, we show that they are equivalent to each other. First we demonstrate that STM predicts local and non-local high-energy corrections to general relativity in 4D, which are identical to those predicted by brane-world models. Secondly, we notice that in brane models the usual matter in 4D is a consequence of the dependence of five-dimensional metrics on the extra coordinate. If the 5D bulk metric is independent of the extra dimension, then the brane is void of matter. Thus, in brane theory matter and geometry are unified, which is exactly the paradigm proposed in STM. Consequently, these two 5D theories share the same concepts and predict the same physics. This is important not only from a theoretical point of view, but also in practice. We propose to use a combination of both methods to alleviate the difficult task of finding solutions on the brane. We show an explicit example that illustrate the feasibility of our proposal.Comment: Typos corrected, three references added. To appear in Mod. Phys. Let

FLRW Universes from "Wave-Like" Cosmologies in 5D

We consider the evolution of a 4D-universe embedded in a five-dimensional (bulk) world with a large extra dimension and a cosmological constant. The cosmology in 5D possesses "wave-like" character in the sense that the metric coefficients in the bulk are functions of the extra coordinate and time in a way similar to a pulse or traveling wave propagating along the fifth dimension. This assumption is motivated by some recent work presenting the big-bang as a higher dimensional shock wave. We show that this assumption, together with an equation of state for the effective matter quantities in 4D, allows Einstein's equations to be fully integrated. We then recover the familiar FLRW universes, on the four-dimensional hypersurfaces orthogonal to the extra dimension. Regarding the extra dimension we find that it is {\em growing} in size if the universe is speeding up its expansion. We also get an estimate for the relative change of the extra dimension over time. This estimate could have important observational implications, notably for the time variation of rest mass, electric charge and the gravitational "constant". Our results extend previous ones in the literature.Comment: Few comments added, references updated. To appear in Int. J. of Mod. Phys.

Extra symmetry in the field equations in 5D with spatial spherical symmetry

We point out that the field equations in 5D, with spatial spherical symmetry, possess an extra symmetry that leaves them invariant. This symmetry corresponds to certain simultaneous interchange of coordinates and metric coefficients. As a consequence a single solution in 5D can generate very different scenarios in 4D, ranging from static configurations to cosmological situations. A new perspective emanates from our work. Namely, that different astrophysical and cosmological scenarios in 4D might correspond to the same physics in 5D. We present explicit examples that illustrate this point of view.Comment: Typos corrected. Accepted for publication in Classical and Quantum Gravit