A topological proof that surface relators are test words

Vegeu el resum a l'inici del document del fitxer adjunt.

Krein's strings whose spectral functions are of polynomial growth

In case Krein's strings with spectral functions of polynomial growth a necessary and su fficient condition for the Krein's correspondence to be continuous is given.

Quantum similarity topological indices definition, analysis and comparison with classical molecular topological indices

Es mostra que, gracies a una extensió en la definició dels Índexs Moleculars Topològics, s'arriba a la formulació d'índexs relacionats amb la teoria de la Semblança Molecular Quàntica. Es posa de manifest la connexió entre les dues metodologies: es revela que un marc de treball teòric sòlidament fonamentat sobre la teoria de la Mecànica Quàntica es pot connectar amb una de les tècniques més antigues relacionades amb els estudis de QSPR. Es mostren els resultats per a dos casos d'exemple d'aplicació d'ambdues metodologies

Topological comparison of methods for predicting transcriptional cooperativity in yeast

Background: The cooperative interaction between transcription factors has a decisive role in the control of the fate of the eukaryotic cell. Computational approaches for characterizing cooperative transcription factors in yeast, however, are based on different rationales and provide a low overlap between their results. Because the wealth of information contained in protein interaction networks and regulatory networks has proven highly effective in elucidating functional relationships between proteins, we compared different sets of cooperative transcription factor pairs (predicted by four different computational methods) within the frame of those networks. Results: Our results show that the overlap between the sets of cooperative transcription factors predicted by the different methods is low yet significant. Cooperative transcription factors predicted by all methods are closer and more clustered in the protein interaction network than expected by chance. On the other hand, members of a cooperative transcription factor pair neither seemed to regulate each other nor shared similar regulatory inputs, although they do regulate similar groups of target genes. Conclusion: Despite the different definitions of transcriptional cooperativity and the different computational approaches used to characterize cooperativity between transcription factors, the analysis of their roles in the framework of the protein interaction network and the regulatory network indicates a common denominator for the predictions under study. The knowledge of the shared topological properties of cooperative transcription factor pairs in both networks can be useful not only for designing better prediction methods but also for better understanding the complexities of transcriptional control in eukaryotes.

Topological computation of local cohomology multiplicities.

We express the Lyubeznik numbers of the local ring of a complex isolated singularity in terms of Betti numbers of the associated real link.

Edge excitations and topological order in rotating Bose gas

The edge excitations and related topological orders of correlated states of a fast rotating Bose gas are studied. Using exact diagonalization of small systems, we compute the energies and number of edge excitations, as well as the boson occupancy near the edge for various states. The chiral Luttinger-liquid theory of Wen is found to be a good description of the edges of the bosonic Laughlin and other states identified as members of the principal Jain sequence for bosons. However, we find that in a harmonic trap the edge of the state identified as the Moore-Read (Pfaffian) state shows a number of anomalies. An experimental way of detecting these correlated states is also discussed.

Topological magnetic irreversibility in superconducting Pb samples of various shapes

The magnetic-field dependence of the magnetization of cylinders, disks, and spheres of pure type-I superconducting lead was investigated by means of isothermal measurements of first magnetization curves and hysteresis cycles. Depending on the geometry of the sample and the direction and intensity of the applied magnetic field, the intermediate state exhibits different irreversible features that become particularly highlighted in minor hysteresis cycles. The irreversibility is noticeably observed in cylinders and disks only when the magnetic field is parallel to the axis of revolution and is very subtle in spheres. When the magnetic field decreases from the normal state, the irreversibility appears at a temperature-dependent value whose distance to the thermodynamic critical field depends on the sample geometry. The irreversible features in the disks are altered when they are submitted to an annealing process. These results agree well with very recent high-resolution magneto-optical experiments in similar materials that were interpreted in terms of transitions between different topological structures for the flux configuration in the intermediate state. A discussion of the relative role of geometrical barriers for flux entry and exit and pinning effects as responsible for the magnetic irreversibility is given.

Perturbations on domain walls and strings: A covariant theory

A covariant formalism is developed for describing perturbations on vacuum domain walls and strings. The treatment applies to arbitrary domain walls in (N+1)-dimensional flat spacetime, including the case of bubbles of a true vacuum nucleating in a false vacuum. Straight strings and planar walls in de Sitter space, as well as closed strings and walls nucleating during inflation, are also considered. Perturbations are represented by a scalar field defined on the unperturbed wall or string world sheet. In a number of interesting cases, this field has a tachyonic mass and a nonminimal coupling to the world-sheet curvature.

Quantum fluctuations on domain walls, strings, and vacuum bubbles

We develop a covariant quantum theory of fluctuations on vacuum domain walls and strings. The fluctuations are described by a scalar field defined on the classical world sheet of the defects. We consider the following cases: straight strings and planar walls in flat space, true vacuum bubbles nucleating in false vacuum, and strings and walls nucleating during inflation. The quantum state for the perturbations is constructed so that it respects the original symmetries of the classical solution. In particular, for the case of vacuum bubbles and nucleating strings and walls, the geometry of the world sheet is that of a lower-dimensional de Sitter space, and the problem reduces to the quantization of a scalar field of tachyonic mass in de Sitter space. In all cases, the root-mean-squared fluctuation is evaluated in detail, and the physical implications are briefly discussed.

Black holes from nucleating strings

We evaluate the probability that a loop of string that has spontaneously nucleated during inflation will form a black hole upon collapse, after the end of inflation. We then use the observational bounds on the density of primordial black holes to put constraints on the parameters of the model. Combining these constraints with current upper limits on the expansion rate during inflation, we conclude that the density of black holes formed from nucleating strings is too low to be observed. Also, constraints on domain wall nucleation and monopole pair production during inflation are briefly discussed.

Black holes as fundamental strings: Comparing the absorption of scalars

The recently proposed correspondence principle of Horowitz and Polchinski provides a concrete means to relate (among others) black holes with electric Neveu-SchwarzNeveu-Schwarz charges to fundamental strings and correctly match their entropies. We further test this correspondence by examining the greybody factors in the absorption rates of neutral, minimally coupled scalars by a near extremal black hole. Perhaps surprisingly, the results disagree in general with the absorption by weakly coupled strings. Though this does not disprove the correspondence, it indicates that it might not be simple in this region of the black hole parameter space.