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.

Pulsating strings in Lunin-Maldacena backgrounds

We consider pulsating strings in Lunin-Maldacena backgrounds, specifically in deformed Minkowski spacetime and deformed AdS(5) x S(5). We find the relation between the energy and the oscillation number of the pulsating string when the deformation is small. Since the oscillation number is an adiabatic invariant it can be used to explore the regime of highly excited string states. We then quantize the string and look for such a sector. For the deformed Minkowski background we find a precise match with the classical results if the oscillation number is quantized as an even number. For the deformed AdS(5) x S(5) we find a contribution which depends on the deformation parameter.

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.

Classical strings in AdS(4) x CP(3) with three angular momenta

In this paper, rotating strings in three directions of AdS(4) x CP(3) geometry are studied; its divergent energy limit, and conserved charges are also determined. An interpretation of these configurations as either giant magnons or spiky strings is discussed.

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.

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.

ALGEBRAIC AND GEOMETRIC THEORY OF THE TOPOLOGICAL RING OF COLOMBEAU GENERALIZED FUNCTIONS

We continue the investigation of the algebraic and topological structure of the algebra of Colombeau generalized functions with the aim of building up the algebraic basis for the theory of these functions. This was started in a previous work of Aragona and Juriaans, where the algebraic and topological structure of the Colombeau generalized numbers were studied. Here, among other important things, we determine completely the minimal primes of (K) over bar and introduce several invariants of the ideals of 9(Q). The main tools we use are the algebraic results obtained by Aragona and Juriaans and the theory of differential calculus on generalized manifolds developed by Aragona and co-workers. The main achievement of the differential calculus is that all classical objects, such as distributions, become Cl-functions. Our purpose is to build an independent and intrinsic theory for Colombeau generalized functions and place them in a wider context.

Cheaters in mutualism networks

Mutualism-network studies assume that all interacting species are mutualistic partners and consider that all links are of one kind. However, the influence of different types of links, such as cheating links, on network organization remains unexplored. We studied two flower-visitation networks (Malpighiaceae and Bignoniaceae and their flower visitors), and divide the types of link into cheaters (i.e. robbers and thieves of flower rewards) and effective pollinators. We investigated if there were topological differences among networks with and without cheaters, especially with respect to nestedness and modularity. The Malpighiaceae network was nested, but not modular, and it was dominated by pollinators and had much fewer cheater species than Bignoniaceae network (28% versus 75%). The Bignoniaceae network was mainly a plant-cheater network, being modular because of the presence of pollen robbers and showing no nestedness. In the Malpighiaceae network, removal of cheaters had no major consequences for topology. In contrast, removal of cheaters broke down the modularity of the Bignoniaceae network. As cheaters are ubiquitous in all mutualisms, the results presented here show that they have a strong impact upon network topology.

What makes a species central in a cleaning mutualism network?

Mutualisms often form networks of interacting species, characterized by the existence of a central core of species that potentially drive the ecology and the evolution of the whole community. Centrality measures allow quantification of how central or peripheral a species is within a network, thus informing about the role of each species in network organization, dynamics, and stability. In the present study we addressed the question whether the structural position of species in the network (i.e. their topological importance) relates to their ecological traits. We studied interactions between cleaner and client reef fishes to identify central and peripheral species within a mutualistic network, and investigated five ecological correlates. We used three measures to estimate the level of centrality of a species for distinct structural patterns, such as the number of interactions and the structural proximity to other species. Through the use of a principal component analysis (PCA) we observed that the centrality measures were highly correlated (92.5%) in the studied network, which indicates that the same species plays a similar role for the different structural patterns. Three cleaner and ten client species had positive values of centrality, which suggests that these species are modulating ecological and evolutionary dynamics within the network. Higher centralities were related to higher abundances and feeding habits for client fishes, but not for cleaners. The high correlation between centrality measures in the present study is likely related to the nested structure of the cleaning network. The cleaner species` set, by having central species that are not necessarily the most abundant ones, bears potentially more vulnerable points for network cohesiveness. Additionally, the present study generalizes previous findings for plant-animal mutualisms, as it shows that the structure of marine mutualisms is also related to a complex interplay between abundance and niche-related features.

The nested assembly of individual-resource networks

P>1. Much of the current understanding of ecological systems is based on theory that does not explicitly take into account individual variation within natural populations. However, individuals may show substantial variation in resource use. This variation in turn may be translated into topological properties of networks that depict interactions among individuals and the food resources they consume (individual-resource networks). 2. Different models derived from optimal diet theory (ODT) predict highly distinct patterns of trophic interactions at the individual level that should translate into distinct network topologies. As a consequence, individual-resource networks can be useful tools in revealing the incidence of different patterns of resource use by individuals and suggesting their mechanistic basis. 3. In the present study, using data from several dietary studies, we assembled individual-resource networks of 10 vertebrate species, previously reported to show interindividual diet variation, and used a network-based approach to investigate their structure. 4. We found significant nestedness, but no modularity, in all empirical networks, indicating that (i) these populations are composed of both opportunistic and selective individuals and (ii) the diets of the latter are ordered as predictable subsets of the diets of the more opportunistic individuals. 5. Nested patterns are a common feature of species networks, and our results extend its generality to trophic interactions at the individual level. This pattern is consistent with a recently proposed ODT model, in which individuals show similar rank preferences but differ in their acceptance rate for alternative resources. Our findings therefore suggest a common mechanism underlying interindividual variation in resource use in disparate taxa.