Global Topological Features Research Articles

Immersive graph-based visualization and exploration of biological data relationships

Genomic information shows some characteristics that make them very difficult to interpret and to exploit. Such data constitute an important factual resource (GenBank, SwissProt, GeneOntology, or Decrypthon…), are heterogeneous, huge in quantity, and geographically distributed. This paper presents Genome3DExplorer, a new modeling and software solution to visualize textual and factual genomic data based on adapted federator description language. The exploration is based on a well-adapted graphical paradigm that automatically helps to build a graph-based representation, and allows biologist to highlight some global topological characteristics of data, which are uneasily visible using traditional exploration tools. Finally, we present results produced by Genome3DExplorer software on various sets of biological data.

Fractal analysis of protein potential energy landscapes

The fractal properties of the total potential energy V as a function of time t are studied for a number of systems, including realistic models of proteins (PPT, BPTI and myoglobin). The fractal dimension of V(t), characterized by the exponent \gamma, is almost independent of temperature and increases with time, more slowly the larger the protein. Perhaps the most striking observation of this study is the apparent universality of the fractal dimension, which depends only weakly on the type of molecular system. We explain this behavior by assuming that fractality is caused by a self-generated dynamical noise, a consequence of intermode coupling due to anharmonicity. Global topological features of the potential energy landscape are found to have little effect on the observed fractal behavior.

Branes: from free fields to general backgrounds

Motivated by recent developments in string theory, we study the structure of boundary conditions in arbitrary conformal field theories. A boundary condition is specified by two types of data: first, a consistent collection of reflection coefficients for bulk fields on the disk; and second, a choice of an automorphism ω of the fusion rules that preserves conformal weights and can be implemented on the spaces of chiral blocks. Non-trivial automorphisms ω correspond to D-brane configurations for arbitrary conformal field theories. The choice of the fusion rule automorphism ω amounts to fixing the dimension and certain global topological features of the D-brane world volume and the background gauge field on it. We present evidence that for fixed choice of ω the boundary conditions are classified as the irreducible representations of some commutative associative algebra, a generalization of the fusion rule algebra. Each of these irreducible representations corresponds to a choice of the moduli for the world volume of the D-brane and the moduli of the flat connection on it.

A description of characteristic classes of real submanifolds in complex manifolds via RC-singularities

Let be a complex manifold, a (closed, orient) real submanifold, and the set of RC-singular points of . We study the connection between the global topological characteristics of and the topology of and . For the case of discrete we introduce a notion of an isolate RC-singular point and obtain a formula expressing the sun of indices over in terms of the Chern classes of and the Pontryagin classes of and of the normal bundle to in (Theorem 1). In the general case we express the Poincare dual to (Theorem 2) and the Poincare duals to some cycles carried by subsets of (Theorem 3) in a similar way.

Topological effects due to a cosmic string

A quantum particle is considered in the background spacetime generated by a cosmic string. It is shown that in the locally flat spacetime around the cosmic string, the wavefunction and the energy spectrum depend on the mass density of the string. These effects are due to global (topological) features of the spacetime generated by the cosmic string.

Gravitational analogs of the Aharonov–Bohm effect

A quantum scalar particle is considered in the following background gravitational fields due to (a) a tubular matter source with axial interior magnetic field and vanishing exterior magnetic field; (b) slowly moving mass currents (weak approximation); and (c) a spinning cosmic string. It is shown that in the flat space-time around these sources, the energy spectrum and wave function of the particle depend on the amount of matter and magnetic field (tubular matter source case), on the velocity of the moving mass currents, and on the angular momentum in the spinning cosmic string case. These represent gravitational analogs of the Aharonov–Bohm effect in electrodynamics and are due to global (topological) features of the background space-times under consideration.