Planar resonant periodic orbits in Kuiper belt dynamics

In the framework of the planar restricted three body problem we study a considerable number of resonances associated to the Kuiper Belt dynamics and located between 30 and 48 a.u. Our study is based on the computation of resonant periodic orbits and their stability. Stable periodic orbits are surrounded by regular librations in phase space and in such domains the capture of trans-Neptunian object is possible. All the periodic orbits found are symmetric and there is evidence for the existence of asymmetric ones only in few cases. In the present work first, second and third order resonances are under consideration. In the planar circular case we found that most of the periodic orbits are stable. The families of periodic orbits are temporarily interrupted by collisions but they continue up to relatively large values of the Jacobi constant and highly eccentric regular motion exists for all cases. In the elliptic problem and for a particular eccentricity value of the primary bodies the periodic orbits are isolated. The corresponding families, where they belong to, bifurcate from specific periodic orbits of the circular problem and seem to continue up to the rectilinear problem. Both stable and unstable orbits are obtained for each case. In the elliptic problem the unstable orbits found are associated with narrow chaotic domains in phase space. The evolution of the orbits, which are located in such chaotic domains, seems to be practically regular and bounded for long time intervals.Comment: preprint, 20 pages, 10 figure

Large-scale Parallel Stratified Defeasible Reasoning

We are recently experiencing an unprecedented explosion of available data from the Web, sensors readings, scientific databases, government authorities and more. Such datasets could benefit from the introduction of rule sets encoding commonly accepted rules or facts, application- or domain-specific rules, commonsense knowledge etc. This raises the question of whether, how, and to what extent knowledge representation methods are capable of handling huge amounts of data for these applications. In this paper, we consider inconsistency-tolerant reasoning in the form of defeasible logic, and analyze how parallelization, using the MapReduce framework, can be used to reason with defeasible rules over huge datasets. We extend previous work by dealing with predicates of arbitrary arity, under the assumption of stratification. Moving from unary to multi-arity predicates is a decisive step towards practical applications, e.g. reasoning with linked open (RDF) data. Our experimental results demonstrate that defeasible reasoning with millions of data is performant, and has the potential to scale to billions of facts

Scalable RDF Data Compression using X10

The Semantic Web comprises enormous volumes of semi-structured data elements. For interoperability, these elements are represented by long strings. Such representations are not efficient for the purposes of Semantic Web applications that perform computations over large volumes of information. A typical method for alleviating the impact of this problem is through the use of compression methods that produce more compact representations of the data. The use of dictionary encoding for this purpose is particularly prevalent in Semantic Web database systems. However, centralized implementations present performance bottlenecks, giving rise to the need for scalable, efficient distributed encoding schemes. In this paper, we describe an encoding implementation based on the asynchronous partitioned global address space (APGAS) parallel programming model. We evaluate performance on a cluster of up to 384 cores and datasets of up to 11 billion triples (1.9 TB). Compared to the state-of-art MapReduce algorithm, we demonstrate a speedup of 2.6-7.4x and excellent scalability. These results illustrate the strong potential of the APGAS model for efficient implementation of dictionary encoding and contributes to the engineering of larger scale Semantic Web applications

Motion on a given surface: potentials producing geodesic lines as trajectories

In the light of inverse problem of dynamics, we consider the motion of a material point on an arbitrary two-dimensional surface, submersed in OE3. We study twodimensional potentials which produce a mono-parametric family of geodesic lines as trajectories. We establish a new, non-linear partial differential condition for the potential function V = V(u, v). With the aid of this condition, we examine if a given potential produces a family of geodesic lines on a certain surface or not. On the other hand, we can check if a given family of regular orbits is indeed a family of geodesic lines on a certain surface and then find the potential function V = V(u, v) which gives rise to this family of orbits. Special cases are also studied and pertinent examples are worked out

Improved 2-D vector field reconstruction using virtual sensors and the Radon transform

This paper describes a method that allows one to recover both components of a 2-D vector field based on boundary information only, by solving a system of linear equations. The analysis is carried out in the digital domain and takes advantage of the redundancy in the boundary data, since these may be viewed as weighted sums of the local vector field’s Cartesian components. Furthermore, a sampling of lines is used in order to combine the available measurements along continuous tracing lines with the digitised 2-D space where the solution is sought. A significant enhancement in the performance of the proposed algorithm is achieved by using, apart from real data, also boundary data obtained at virtual sensors. The potential of the proposed method is demonstrated by presenting an example of vector field reconstruction

Virtual sensors for 2D vector field tomography

We consider the application of tomography to the reconstruction of 2-D vector fields. The most convenient sensor configuration in such problems is the regular positioning along the domain boundary. However, the most accurate reconstructions are obtained by sampling uniformly the Radon parameter domain rather than the border of the reconstruction domain. This dictates a prohibitively large number of sensors and impractical sensor positioning. In this paper, we propose uniform placement of the sensors along the boundary of the reconstruction domain and interpolation of the measurements for the positions that correspond to uniform sampling in the Radon domain. We demonstrate that when the cubic spline interpolation method is used, a 60 times reduction in the number of sensors may be achieved with only about 10% increase in the error with which the vector field is estimated. The reconstruction error by using the same sensors and ignoring the necessity of uniform sampling in the Radon domain is in fact higher by about 30%. The effects of noise are also examined

Genetic structure of the common sole Solea vulgaris at different geographic scales

The genetic structure of the flatfish #Solea vulgaris was investigated on several spatial scales and at the temporal level through analysis of electrophoretic variation at 8 to 12 polymorphic enzyme loci. No differentiation was apparent at the temporal scale. Some differentiation was detected at and above the regional scale. Isolation by distance was evidenced by the significant correlation between genetic and geographic distances, and by the consistency of the results of multiple-locus correspondence analysis with geographic sampling patterns. The analysis suggested that the geographic unit of population structure (i.e. a geographical area corresponding to a panmictic or nearly panmictic population) lies within a radius of the order of 100 km. The isolation-by-distance pattern in #S. vulgaris contrasted with the known genetic structures of other flatfish species of the northeastern Atlantic and Mediterranean in a way that may be related to the range of their respective temperature tolerances for eggs and larvae. (Résumé d'auteur

Three-dimensional potentials producing families of straight lines (FSL)

We identify a given two-parametric family of regular orbits in the 3-D Cartesian space by two functions α and β. Then, from the inverse-problem viewpoint, we find three necessary and sufficient conditions that the functions α and β must satisfy when the given family is a two-parametric family of straight lines (FSL) and is actually created by a potential V. Some pertinent theorems are shown and several examples are worked out