Structuring and support by Alfven waves around prestellar cores

Observations of molecular clouds show the existence of starless, dense cores, threaded by magnetic fields. Observed line widths indicate these dense condensates to be embedded in a supersonically turbulent environment. Under these conditions, the generation of magnetic waves is inevitable. In this paper, we study the structure and support of a 1D plane-parallel, self-gravitating slab, as a monochromatic, circularly polarized Alfven wave is injected in its central plane. Dimensional analysis shows that the solution must depend on three dimensionless parameters. To study the nonlinear, turbulent evolution of such a slab, we use 1D high resolution numerical simulations. For a parameter range inspired by molecular cloud observations, we find the following. 1) A single source of energy injection is sufficient to force persistent supersonic turbulence over several hydrostatic scale heights. 2) The time averaged spatial extension of the slab is comparable to the extension of the stationary, analytical WKB solution. Deviations, as well as the density substructure of the slab, depend on the wave-length of the injected wave. 3) Energy losses are dominated by loss of Poynting-flux and increase with increasing plasma beta. 4) Good spatial resolution is mandatory, making similar simulations in 3D currently prohibitively expensive.Comment: 13 pages, 8 figures, accepted for publication in A&A. The manuscript with full color, high-resolution, figures can be downloaded from http://www.astro.phys.ethz.ch/papers/folini/folini_p_nf.htm

Support Vector Machines for Business Applications

This chapter discusses the usage of Support Vector Machines (SVM) for business applications. It provides a brief historical background on inductive learning and pattern recognition, and then an intuitive motivation for SVM methods. The method is compared to other approaches, and the tools and background theory required to successfully apply SVMs to business applications are introduced. The authors hope that the chapter will help practitioners to understand when the SVM should be the method of choice, as well as how to achieve good results in minimal time

Homogenised Virtual Support Vector Machines

In many domains, reliable a priori knowledge exists that may be used to improve classifier performance. For example in handwritten digit recognition, such a priori knowledge may include classification invariance with respect to image translations and rotations. In this paper, we present a new generalisation of the Support Vector Machine (SVM) that aims to better incorporate this knowledge. The method is an extension of the Virtual SVM, and penalises an approximation of the variance of the decision function across each grouped set of "virtual examples", thus utilising the fact that these groups should ideally be assigned similar class membership probabilities. The method is shown to be an efficient approximation of the invariant SVM of Chapelle and Scholkopf, with the advantage that it can be solved by trivial modification to standard SVM optimization packages and negligible increase in computational complexity when compared with the Virtual SVM. The efficacy of the method is demonstrated on a simple problem

Face and Object Recognition and Detection Using Colour Vector Quantisation

In this paper we present an approach to face and object detection and recognition based on an extension of the contentbased image retrieval method of Lu and Teng (1999). The method applies vector quantisation (VQ) compression to the image stream and uses Mahalonobis weighted Euclidean distance between VQ histograms as the measure of image similarity. This distance measure retains both colour and spatial feature information but has the useful property of being relatively insensitive to changes in scale and rotation. The method is applied to real images for face recognition and face detection applications. Tracking and object detection can be coded relatively efficiently due to the data reduction afforded by VQ compression of the data stream. Additional computational efficiency is obtained through a variation of the tree structured fast VQ algorithm also presented here

Kernel Based Algebraic Curve Fitting

An algebraic curve is defined as the zero set of a multivariate polynomial. We consider the problem of fitting an algebraic curve to a set of vectors given an additional set of vectors labelled as interior or exterior to the curve. The problem of fitting a linear curve in this way is shown to lend itself to a support vector representation, allowing non-linear curves and high dimensional surfaces to be estimated using kernel functions. The approach is attractive due to the stability of solutions obtained, the range of functional forms made possible (including polynomials), and the potential for applying well understood regularisation operators from the theory of Support Vector Machines

Lithium depletion in solar-like stars: effect of overshooting based on realistic multi-dimensional simulations

We study lithium depletion in low-mass and solar-like stars as a function of time, using a new diffusion coefficient describing extra-mixing taking place at the bottom of a convective envelope. This new form is motivated by multi-dimensional fully compressible, time implicit hydrodynamic simulations performed with the MUSIC code. Intermittent convective mixing at the convective boundary in a star can be modeled using extreme value theory, a statistical analysis frequently used for finance, meteorology, and environmental science. In this letter, we implement this statistical diffusion coefficient in a one-dimensional stellar evolution code, using parameters calibrated from multi-dimensional hydrodynamic simulations of a young low-mass star. We propose a new scenario that can explain observations of the surface abundance of lithium in the Sun and in clusters covering a wide range of ages, from $\sim$ 50 Myr to $\sim$ 4 Gyr. Because it relies on our physical model of convective penetration, this scenario has a limited number of assumptions. It can explain the observed trend between rotation and depletion, based on a single additional assumption, namely that rotation affects the mixing efficiency at the convective boundary. We suggest the existence of a threshold in stellar rotation rate above which rotation strongly prevents the vertical penetration of plumes and below which rotation has small effects. In addition to providing a possible explanation for the long standing problem of lithium depletion in pre-main sequence and main sequence stars, the strength of our scenario is that its basic assumptions can be tested by future hydrodynamic simulations.Comment: 7 pages, 3 figures, Accepted for publication in ApJ Letter

Implicit Surface Modelling as an Eigenvalue Problem

We discuss the problem of fitting an implicit shape model to a set of points sampled from a co-dimension one manifold of arbitrary topology. The method solves a non-convex optimisation problem in the embedding function that defines the implicit by way of its zero level set. By assuming that the solution is a mixture of radial basis functions of varying widths we attain the globally optimal solution by way of an equivalent eigenvalue problem, without using or constructing as an intermediate step the normal vectors of the manifold at each data point. We demonstrate the system on two and three dimensional data, with examples of missing data interpolation and set operations on the resultant shapes

Towards a Maximum Entropy Method for Estimating HMM Parameters

Training a Hidden Markov Model (HMM) to maximise the probability of a given sequence can result in over-fitting. That is, the model represents the training sequence well, but fails to generalise. In this paper, we present a possible solution to this problem, which is to maximise a linear combination of the likelihood of the training data, and the entropy of the model. We derive the necessary equations for gradient based maximisation of this combined term. The performance of the system is then evaluated in comparison with three other algorithms, on a classification task using synthetic data. The results indicate that the method is potentially useful. The main problem with the method is the computational intractability of the entropy calculation