Topological multi-contour decomposition for image analysis and image retrieval

Successful classification, information retrieval and image analysis tools are intimately related with the quality of the features employed in the process. Pixel intensities, color, texture and shape are, generally, the basis from which most of the features are Computed and used in such fields. This papers presents a novel shape-based feature extraction approach where an image is decomposed into multiple contours, and further characterized by Fourier descriptors. Unlike traditional approaches we make use of topological knowledge to generate well-defined closed contours, which are efficient signatures for image retrieval. The method has been evaluated in the CBIR context and image analysis. The results have shown that the multi-contour decomposition, as opposed to a single shape information, introduced a significant improvement in the discrimination power. (c) 2008 Elsevier B.V. All rights reserved,

Topological invariants of isolated complete intersection curve singularities

In this paper we present some formulae for topological invariants of projective complete intersection curves with isolated singularities in terms of the Milnor number, the Euler characteristic and the topological genus. We also present some conditions, involving the Milnor number and the degree of the curve, for the irreducibility of complete intersection curves.

Topological triangle characterization with application to object detection from images

A novel mathematical framework inspired on Morse Theory for topological triangle characterization in 2D meshes is introduced that is useful for applications involving the creation of mesh models of objects whose geometry is not known a priori. The framework guarantees a precise control of topological changes introduced as a result of triangle insertion/removal operations and enables the definition of intuitive high-level operators for managing the mesh while keeping its topological integrity. An application is described in the implementation of an innovative approach for the detection of 2D objects from images that integrates the topological control enabled by geometric modeling with traditional image processing techniques. (C) 2008 Published by Elsevier B.V.

EXPLOITING A GENERIC APPROACH TO CONSTRUCT COMPONENT-BASED SYSTEMS SOFTWARE IN LINUX ENVIRONMENTS

Component-based software engineering has recently emerged as a promising solution to the development of system-level software. Unfortunately, current approaches are limited to specific platforms and domains. This lack of generality is particularly problematic as it prevents knowledge sharing and generally drives development costs up. In the past, we have developed a generic approach to component-based software engineering for system-level software called OpenCom. In this paper, we present OpenComL an instantiation of OpenCom to Linux environments and show how it can be profiled to meet a range of system-level software in Linux environments. For this, we demonstrate its application to constructing a programmable router platform and a middleware for parallel environments.

Topological interactions in warped extra dimensions

Topological interactions will be generated in theories with compact extra dimensions where fermionic chiral zero modes have different localizations. This is the case in many warped extra dimension models where the right-handed top quark is typically localized away from the left-handed one. Using deconstruction techniques, we study the topological interactions in these models. These interactions appear as trilinear and quadrilinear gauge boson couplings in low energy effective theories with three or more sites, as well as in the continuum limit. We derive the form of these interactions for various cases, including examples of Abelian, non-Abelian and product gauge groups of phenomenological interest. The topological interactions provide a window into the more fundamental aspects of these theories and could result in unique signatures at the Large Hadron Collider, some of which we explore.

Weak antilocalization in HgTe quantum wells near a topological transition

The anomalous alternating magnetoresistivity in HgTe quantum wells with thicknesses of 5.8 and 8.3 nm, i.e., near the transition from the direct band spectrum to an inverted spectrum, has been revealed and analyzed. It has been shown that the revealed anomalous alternating magnetoresistivity in wells with an inverted spectrum is well described by the theory developed by S.V. Iordanskii et al. [JETP Lett. 60, 206 (1994)] and W. Knap et al. [Phys. Rev. B 53, 3912 (1996)]. A detailed comparison of the experimental data with the theory indicates the presence of only the cubic term in the spin splitting of the electronic spectrum. The applicability conditions of the mentioned theory are not satisfied in a well with a direct gap and, for this reason, such a certain conclusion is impossible. The results indicate the existence of a strong spin-orbit interaction in symmetric HgTe quantum wells near the topological transition.

Coherent and semiclassical states in a magnetic field in the presence of the Aharonov-Bohm solenoid

A new approach to constructing coherent states (CS) and semiclassical states (SS) in a magnetic-solenoid field is proposed. The main idea is based on the fact that the AB solenoid breaks the translational symmetry in the xy-plane; this has a topological effect such that there appear two types of trajectories which embrace and do not embrace the solenoid. Due to this fact, one has to construct two different kinds of CS/SS which correspond to such trajectories in the semiclassical limit. Following this idea, we construct CS in two steps, first the instantaneous CS (ICS) and then the time-dependent CS/SS as an evolution of the ICS. The construction is realized for nonrelativistic and relativistic spinning particles both in (2 + 1) and (3 + 1) dimensions and gives a non-trivial example of SS/CS for systems with a nonquadratic Hamiltonian. It is stressed that CS depending on their parameters (quantum numbers) describe both pure quantum and semiclassical states. An analysis is represented that classifies parameters of the CS in such respect. Such a classification is used for the semiclassical decompositions of various physical quantities.

Self-dual hopfions

We construct static and time-dependent exact soliton solutions with nontrivial Hopf topological charge for a field theory in 3 + 1 dimensions with the target space being the two dimensional sphere S(2). The model considered is a reduction of the so-called extended Skyrme-Faddeev theory by the removal of the quadratic term in derivatives of the fields. The solutions are constructed using an ansatz based on the conformal and target space symmetries. The solutions are said self-dual because they solve first order differential equations which together with some conditions on the coupling constants, imply the second order equations of motion. The solutions belong to a sub-sector of the theory with an infinite number of local conserved currents. The equation for the profile function of the ansatz corresponds to the Bogomolny equation for the sine-Gordon model.

Static Hopfions in the extended Skyrme-Faddeev model

We construct static soliton solutions with non-zero Hopf topological charges to a theory which is an extension of the Skyrme-Faddeev model by the addition of a further quartic term in derivatives. We use an axially symmetric ansatz based on toroidal coordinates, and solve the resulting two coupled non-linear partial differential equations in two variables by a successive over-relaxation (SOR) method. We construct numerical solutions with Hopf charge up to four, and calculate their analytical behavior in some limiting cases. The solutions present an interesting behavior under the changes of a special combination of the coupling constants of the quartic terms. Their energies and sizes tend to zero as that combination approaches a particular special value. We calculate the equivalent of the Vakulenko and Kapitanskii energy bound for the theory and find that it vanishes at that same special value of the coupling constants. In addition, the model presents an integrable sector with an in finite number of local conserved currents which apparently are not related to symmetries of the action. In the intersection of those two special sectors the theory possesses exact vortex solutions (static and time dependent) which were constructed in a previous paper by one of the authors. It is believed that such model describes some aspects of the low energy limit of the pure SU(2) Yang-Mills theory, and our results may be important in identifying important structures in that strong coupling regime.

Exact vortex solutions in an extended Skyrme-Faddeev model

We construct exact vortex solutions in 3+1 dimensions to a theory which is an extension, due to Gies, of the Skyrme-Faddeev model, and that is believed to describe some aspects of the low energy limit of the pure SU(2) Yang-Mills theory. Despite the efforts in the last decades those are the first exact analytical solutions to be constructed for such type of theory. The exact vortices appear in a very particular sector of the theory characterized by special values of the coupling constants, and by a constraint that leads to an infinite number of conserved charges. The theory is scale invariant in that sector, and the solutions satisfy Bogomolny type equations. The energy of the static vortex is proportional to its topological charge, and waves can travel with the speed of light along them, adding to the energy a term proportional to a U(1) No ether charge they create. We believe such vortices may play a role in the strong coupling regime of the pure SU(2) Yang-Mills theory.

Axially symmetric soliton solutions in a Skyrme-Faddeev-type model with Gies`s extension

We construct static soliton solutions with non-zero Hopf topological charges to a theory which is the extended Skyrme-Faddeev model with a further quartic term in derivatives. We use an axially symmetric ansatz based on toroidal coordinates, and solve the resulting two coupled nonlinear partial differential equations in two variables by a successive over-relaxation method. We construct numerical solutions with the Hopf charge up to 4. The solutions present an interesting behavior under the changes of a special combination of the coupling constants of the quartic terms.

Characterizing topological and dynamical properties of complex networks without border effects

The properties of complex networks are highly Influenced by border effects frequently found as a consequence of the finite nature of real-world networks as well as network Sampling Therefore, it becomes critical to devise effective means for sound estimation of net work topological and dynamical properties will le avoiding these types of artifacts. In the current work, an algorithm for minimization of border effects is proposed and discussed, and its potential IS Illustrated with respect to two real-world networks. namely bone canals and air transportation (C) 2009 Elsevier B.V. All rights reserved.

Resilience of protein-protein interaction networks as determined by their large-scale topological features

The relationship between the structure and function of biological networks constitutes a fundamental issue in systems biology. Particularly, the structure of protein-protein interaction networks is related to important biological functions. In this work, we investigated how such a resilience is determined by the large scale features of the respective networks. Four species are taken into account, namely yeast Saccharomyces cerevisiae, worm Caenorhabditis elegans, fly Drosophila melanogaster and Homo sapiens. We adopted two entropy-related measurements (degree entropy and dynamic entropy) in order to quantify the overall degree of robustness of these networks. We verified that while they exhibit similar structural variations under random node removal, they differ significantly when subjected to intentional attacks (hub removal). As a matter of fact, more complex species tended to exhibit more robust networks. More specifically, we quantified how six important measurements of the networks topology (namely clustering coefficient, average degree of neighbors, average shortest path length, diameter, assortativity coefficient, and slope of the power law degree distribution) correlated with the two entropy measurements. Our results revealed that the fraction of hubs and the average neighbor degree contribute significantly for the resilience of networks. In addition, the topological analysis of the removed hubs indicated that the presence of alternative paths between the proteins connected to hubs tend to reinforce resilience. The performed analysis helps to understand how resilience is underlain in networks and can be applied to the development of protein network models.

Paper surfaces and dynamical limits

It is very common in mathematics to construct surfaces by identifying the sides of a polygon together in pairs: For example, identifying opposite sides of a square yields a torus. In this article the construction is considered in the case where infinitely many pairs of segments around the boundary of the polygon are identified. The topological, metric, and complex structures of the resulting surfaces are discussed: In particular, a condition is given under which the surface has a global complex structure (i.e., is a Riemann surface). In this case, a modulus of continuity for a uniformizing map is given. The motivation for considering this construction comes from dynamical systems theory: If the modulus of continuity is uniform across a family of such constructions, each with an iteration defined on it, then it is possible to take limits in the family and hence to complete it. Such an application is briefly discussed.

EQUIVARIANT PATH FIELDS ON TOPOLOGICAL MANIFOLDS

A classical theorem of H. Hopf asserts that a closed connected smooth manifold admits a nowhere vanishing vector field if and only if its Euler characteristic is zero. R. Brown generalized Hopf`s result to topological manifolds, replacing vector fields with path fields. In this note, we give an equivariant analog of Brown`s theorem for locally smooth G-manifolds where G is a finite group.