Automorphism Group of k((t))k((t)): Applications to the Bosonic String

This paper is concerned with the formulation of a non-pertubative theory of the bosonic string. We introduce a formal group $G$ which we propose as the ``universal moduli space'' for such a formulation. This is motivated because $G$ establishes a natural link between representations of the Virasoro algebra and the moduli space of curves. Among other properties of $G$ it is shown that a ``local'' version of the Mumford formula holds on $G$.Comment: 29 page

Vacuum ultraviolet photolysis of hydrogenated amorphous carbons. III. Diffusion of photo-produced H2 as a function of temperature

Hydrogenated amorphous carbon (a-C:H) has been proposed as one of the carbonaceous solids detected in the interstellar medium. Energetic processing of the a-C:H particles leads to the dissociation of the C-H bonds and the formation of hydrogen molecules and small hydrocarbons. Photo-produced H2 molecules in the bulk of the dust particles can diffuse out to the gas phase and contribute to the total H2 abundance. We have simulated this process in the laboratory with plasma-produced a-C:H and a-C:D analogs under astrophysically relevant conditions to investigate the dependence of the diffusion as a function of temperature. Plasma-produced a-C:H analogs were UV-irradiated using a microwave-discharged hydrogen flow lamp. Molecules diffusing to the gas-phase were detected by a quadrupole mass spectrometer, providing a measurement of the outgoing H2 or D2 flux. By comparing the experimental measurements with the expected flux from a one-dimensional diffusion model, a diffusion coefficient D could be derived for experiments carried out at different temperatures. Dependance on the diffusion coefficient D with the temperature followed an Arrhenius-type equation. The activation energy for the diffusion process was estimated (ED(H2)=1660+-110 K, ED(D2)=2090+-90 K), as well as the pre-exponential factor (D0(H2)=0.0007+0.0013-0.0004 cm2 s-1, D0(D2)=0.0045+0.005-0.0023 cm2 s-1) The strong decrease of the diffusion coefficient at low dust particle temperatures exponentially increases the diffusion times in astrophysical environments. Therefore, transient dust heating by cosmic rays needs to be invoked for the release of the photo- produced H2 molecules in cold PDR regions, where destruction of the aliphatic component in hydrogenated amorphous carbons most probably takes place

On the combination of kernels for support vector classifiers

The problem of combining different sources of information arises in several situations, for instance, the classification of data with asymmetric similarity matrices or the construction of an optimal classifier from a collection of kernels. Often, each source of information can be expressed as a kernel (similarity) matrix and, therefore, a collection of kernels is available. In this paper we propose a new class of methods in order to produce, for classification purposes, an unique and optimal kernel. Then, the constructed kernel is used to train a Support Vector Machine (SVM). The key ideas within the kernel construction are two: the quantification, relative to the classification labels, of the difference of information among the kernels; and the extension of the concept of linear combination of kernels to the concept of functional (matrix) combination of kernels. The proposed methods have been successfully evaluated and compared with other powerful classifiers and kernel combination techniques on a variety of artificial and real classification problems

ON THE COMBINATION OF KERNELS FOR SUPPORT VECTOR CLASSIFIERS

The problem of combining different sources of information arises in several situations, for instance, the classification of data with asymmetric similarity matrices or the construction of an optimal classifier from a collection of kernels. Often, each source of information can be expressed as a kernel (similarity) matrix and, therefore, a collection of kernels is available. In this paper we propose a new class of methods in order to produce, for classification purposes, an unique and optimal kernel. Then, the constructed kernel is used to train a Support Vector Machine (SVM). The key ideas within the kernel construction are two: the quantification, relative to the classification labels, of the difference of information among the kernels; and the extension of the concept of linear combination of kernels to the concept of functional (matrix) combination of kernels. The proposed methods have been successfully evaluated and compared with other powerful classifiers and kernel combination techniques on a variety of artificial and real classification problems.