Dynamic picture of the inner asteroid belt: implications for the density, size and taxonomic distributions of real objects

In this paper, we construct a dynamic portrait of the inner asteroidal belt. We use information about the distribution of test particles, which were initially placed on a perfectly rectangular grid of initial conditions, after 4.2 Myr of gravitational interactions with the Sun and five planets, from Mars to Neptune. Using the spectral analysis method introduced by Michtchenko et al., the asteroidal behaviour is illustrated in detail on the dynamical, averaged and frequency maps. On the averaged and frequency maps, we superpose information on the proper elements and proper frequencies of real objects, extracted from the data base, AstDyS, constructed by Milani and Knezevic. A comparison of the maps with the distribution of real objects allows us to detect possible dynamical mechanisms acting in the domain under study; these mechanisms are related to mean-motion and secular resonances. We note that the two- and three-body mean-motion resonances and the secular resonances (strong linear and weaker non-linear) have an important role in the diffusive transportation of the objects. Their long-lasting action, overlaid with the Yarkovsky effect, may explain many observed features of the density, size and taxonomic distributions of the asteroids.

Selecting salient objects in real scenes: An oscillatory correlation model

Attention is a critical mechanism for visual scene analysis. By means of attention, it is possible to break down the analysis of a complex scene to the analysis of its parts through a selection process. Empirical studies demonstrate that attentional selection is conducted on visual objects as a whole. We present a neurocomputational model of object-based selection in the framework of oscillatory correlation. By segmenting an input scene and integrating the segments with their conspicuity obtained from a saliency map, the model selects salient objects rather than salient locations. The proposed system is composed of three modules: a saliency map providing saliency values of image locations, image segmentation for breaking the input scene into a set of objects, and object selection which allows one of the objects of the scene to be selected at a time. This object selection system has been applied to real gray-level and color images and the simulation results show the effectiveness of the system. (C) 2010 Elsevier Ltd. All rights reserved.

A Framework for Exploring Multidimensional Data with 3D Projections

Visualization of high-dimensional data requires a mapping to a visual space. Whenever the goal is to preserve similarity relations a frequent strategy is to use 2D projections, which afford intuitive interactive exploration, e. g., by users locating and selecting groups and gradually drilling down to individual objects. In this paper, we propose a framework for projecting high-dimensional data to 3D visual spaces, based on a generalization of the Least-Square Projection (LSP). We compare projections to 2D and 3D visual spaces both quantitatively and through a user study considering certain exploration tasks. The quantitative analysis confirms that 3D projections outperform 2D projections in terms of precision. The user study indicates that certain tasks can be more reliably and confidently answered with 3D projections. Nonetheless, as 3D projections are displayed on 2D screens, interaction is more difficult. Therefore, we incorporate suitable interaction functionalities into a framework that supports 3D transformations, predefined optimal 2D views, coordinated 2D and 3D views, and hierarchical 3D cluster definition and exploration. For visually encoding data clusters in a 3D setup, we employ color coding of projected data points as well as four types of surface renderings. A second user study evaluates the suitability of these visual encodings. Several examples illustrate the framework`s applicability for both visual exploration of multidimensional abstract (non-spatial) data as well as the feature space of multi-variate spatial data.

Global solutions for impulsive abstract partial differential equations

In this paper, we study the existence of global solutions for a class of impulsive abstract functional differential equation. An application involving a parabolic system With impulses is considered. (c) 2008 Elsevier Ltd. All rights reserved.

Classification of quantum relativistic orientable objects

Extending our previous work `Fields on the Poincare group and quantum description of orientable objects` (Gitman and Shelepin 2009 Eur. Phys. J. C 61 111-39), we consider here a classification of orientable relativistic quantum objects in 3 + 1 dimensions. In such a classification, one uses a maximal set of ten commuting operators (generators of left and right transformations) in the space of functions on the Poincare group. In addition to the usual six quantum numbers related to external symmetries (given by left generators), there appear additional quantum numbers related to internal symmetries (given by right generators). Spectra of internal and external symmetry operators are interrelated, which, however, does not contradict the Coleman-Mandula no-go theorem. We believe that the proposed approach can be useful for the description of elementary spinning particles considered as orientable objects. In particular, it gives a group-theoretical interpretation of some facts of the existing phenomenological classification of spinning particles.

Field on Poincare Group and Quantum Description of Orientable Objects

We propose an approach to the quantum-mechanical description of relativistic orientable objects. It generalizes Wigner`s ideas concerning the treatment of nonrelativistic orientable objects (in particular, a nonrelativistic rotator) with the help of two reference frames (space-fixed and body-fixed). A technical realization of this generalization (for instance, in 3+1 dimensions) amounts to introducing wave functions that depend on elements of the Poincar, group G. A complete set of transformations that test the symmetries of an orientable object and of the embedding space belongs to the group I =GxG. All such transformations can be studied by considering a generalized regular representation of G in the space of scalar functions on the group, f(x,z), that depend on the Minkowski space points xaG/Spin(3,1) as well as on the orientation variables given by the elements z of a matrix ZaSpin(3,1). In particular, the field f(x,z) is a generating function of the usual spin-tensor multi-component fields. In the theory under consideration, there are four different types of spinors, and an orientable object is characterized by ten quantum numbers. We study the corresponding relativistic wave equations and their symmetry properties.