On local comparison between various metrics on Teichmüller spaces

International audienceThere are several Teichmüller spaces associated to a surface of infinite topological type, after the choice of a particular basepoint ( a complex or a hyperbolic structure on the surface). These spaces include the quasiconformal Teichmüller space, the length spectrum Teichmüller space, the Fenchel-Nielsen Teichmüller space, and there are others. In general, these spaces are set-theoretically different. An important question is therefore to understand relations between these spaces. Each of these spaces is equipped with its own metric, and under some hypotheses, there are inclusions between these spaces. In this paper, we obtain local metric comparison results on these inclusions, namely, we show that the inclusions are locally bi-Lipschitz under certain hypotheses. To obtain these results, we use some hyperbolic geometry estimates that give new results also for surfaces of finite type. We recall that in the case of a surface of finite type, all these Teichmüller spaces coincide setwise. In the case of a surface of finite type with no boundary components (and possibly with punctures), we show that the restriction of the identity map to any thick part of Teichmüller space is globally bi-Lipschitz with respect to the length spectrum metric and the classical Teichmüller metric on the domain and on the range respectively. In the case of a surface of finite type with punctures and boundary components, there is a metric on the Teichmüller space which we call the arc metric, whose definition is analogous to the length spectrum metric, but which uses lengths of geodesic arcs instead of lengths of closed geodesics. We show that the restriction of the identity map restricted to any ``relative thick" part of Teichmüller space is globally bi-Lipschitz, with respect to any of the three metrics: the length spectrum metric, the Teichmüller metric and the arc metric on the domain and on the range

Scattering of Glueballs and Mesons in Compact QEDQED in 2+12+1 Dimensions

We study glueball and meson scattering in compact $QED_{2+1}$ gauge theory in a Hamiltonian formulation and on a momentum lattice. We compute ground state energy and mass, and introduce a compact lattice momentum operator for the computation of dispersion relations. Using a non-perturbative time-dependent method we compute scattering cross sections for glueballs and mesons. We compare our results with strong coupling perturbation theory.Comment: figures not included (hard copy only), LAVAL-PHY-94-05, PARKS-PHY-94-0

Glutamate Receptors and Glioblastoma Multiforme: An Old "Route" for New Perspectives

Glioblastoma multiforme (GBM) is the most aggressive malignant tumor of the central nervous system, with poor survival in both treated and untreated patients. Recent studies began to explain the molecular pathway, comprising the dynamic structural and mechanical changes involved in GBM. In this context, some studies showed that the human glioblastoma cells release high levels of glutamate, which regulates the proliferation and survival of neuronal progenitor cells. Considering that cancer cells possess properties in common with neural progenitor cells, it is likely that the functions of glutamate receptors may affect the growth of cancer cells and, therefore, open the road to new and more targeted therapies

On the inclusion of the quasiconformal Teichmüller space into the length-spectrum Teichmüller space

This paper is about surfaces of infinite topological type. Unlike the case of surfaces of finite type, there are several deformation spaces associated with a surface S of infinite topological type. Such spaces depend on the choice of a basepoint (that is, the choice of a fixed conformal structure or hyperbolic structure on S) and they also depend on the choice of a distance on the set of equivalence classes of marked hyperbolic structures. We address the question of the comparison between two deformation spaces, namely, the quasiconformal Teichmüller space and the length-spectrum Teichmüller space. There is a natural inclusion map of the quasiconformal space into the length-spectrum space, which is not always surjective. We work under the hypothesis that the basepoint (a hyperbolic surface) satisfies a condition we call “upper-boundedness”. This means that this surface admits a pants decomposition defined by curves whose lengths are bounded above. The theory under this upper- boundedness hypothesis shows a dichotomy. On the one hand there are surfaces satisfying what we call Shiga’s condition, i.e. they admit a pants decomposition defined by curves whose lengths are bounded above and below. If the base point satisfies Shiga’s condition, then the inclusion of the quasiconformal space into the length- spectrum space is surjective, and it is a homeomorphism. In this paper we concentrate on the other kind of upper-bounded surfaces, which we call “upper-bounded with short interior curves”. This means that the corresponding hyperbolic surface admits a pants decomposition defined by curves whose lengths are bounded above, and such that the lengths of some interior curves approach zero. We show that in this case the behavior is completely different. Under this hypothesis, the image of the inclusion between the two Teichmüller spaces is nowhere dense in the length-spectrum space. As a corollary of the methods used, we obtain an explicit parametrization of the length-spectrum Teichmüller space in terms of Fenchel–Nielsen coordinates and we prove that the length-spectrum Teichmüller space is path-connected

Path integral evaluation of Dbrane amplitudes

We extend Polchinski's evaluation of the measure for the one-loop closed string path integral to open string tree amplitudes with boundaries and crosscaps embedded in Dbranes. We explain how the nonabelian limit of near-coincident Dbranes emerges in the path integral formalism. We give a careful path integral derivation of the cylinder amplitude including the modulus dependence of the volume of the conformal Killing group.Comment: Extended version replacing hep-th/9903184, includes discussion of nonabelian limit, Latex, 10 page

Nonlinear Dynamic System Identification in the Spectral Domain Using Particle-Bernstein Polynomials

System identification (SI) is the discipline of inferring mathematical models from unknown dynamic systems using the input/output observations of such systems with or without prior knowledge of some of the system parameters. Many valid algorithms are available in the literature, including Volterra series expansion, Hammerstein–Wiener models, nonlinear auto-regressive moving average model with exogenous inputs (NARMAX) and its derivatives (NARX, NARMA). Different nonlinear estimators can be used for those algorithms, such as polynomials, neural networks or wavelet networks. This paper uses a different approach, named particle-Bernstein polynomials, as an estimator for SI. Moreover, unlike the mentioned algorithms, this approach does not operate in the time domain but rather in the spectral components of the signals through the use of the discrete Karhunen–Loève transform (DKLT). Some experiments are performed to validate this approach using a publicly available dataset based on ground vibration tests recorded from a real F-16 aircraft. The experiments show better results when compared with some of the traditional algorithms, especially for large, heterogeneous datasets such as the one used. In particular, the absolute error obtained with the prosed method is 63% smaller with respect to NARX and from 42% to 62% smaller with respect to various artificial neural network-based approaches

The stability for the Cauchy problem for elliptic equations

We discuss the ill-posed Cauchy problem for elliptic equations, which is pervasive in inverse boundary value problems modeled by elliptic equations. We provide essentially optimal stability results, in wide generality and under substantially minimal assumptions. As a general scheme in our arguments, we show that all such stability results can be derived by the use of a single building brick, the three-spheres inequality.Comment: 57 pages, review articl

The occurrence of Brassica montana Pourr. (Brassicaceae) in the Italian regions of Emilia-Romagna and Marche, and in the Republic of San Marino

Brassica montana Pourr., a wild relative of the Brassica oleracea L. cole crops (broccoli, cabbage, cauliflower, etc.), deserves special attention for its potential to easily transfer agronomically useful traits to related crops. Monitoring existing B. montana populations is the first step to enabling long-term conservation and management of wild genetic resources. In this paper, we focus on all the B. montana reports for the Italian regions of Emilia-Romagna and Marche, and additionally for the neighbouring Republic of San Marino. According to our analysis, the presence of B. montana is confirmed in the Marche and the Republic of San Marino, but not in Emilia-Romagna