A CASE STUDY ON SUPPORT VECTOR MACHINES VERSUS ARTIFICIAL NEURAL NETWORKS

The capability of artificial neural networks for pattern recognition of real world problems is well known. In recent years, the support vector machine has been advocated for its structure risk minimization leading to tolerance margins of decision boundaries. Structures and performances of these pattern classifiers depend on the feature dimension and training data size. The objective of this research is to compare these pattern recognition systems based on a case study. The particular case considered is on classification of hypertensive and normotensive right ventricle (RV) shapes obtained from Magnetic Resonance Image (MRI) sequences. In this case, the feature dimension is reasonable, but the available training data set is small, however, the decision surface is highly nonlinear.For diagnosis of congenital heart defects, especially those associated with pressure and volume overload problems, a reliable pattern classifier for determining right ventricle function is needed. RV¡¦s global and regional surface to volume ratios are assessed from an individual¡¦s MRI heart images. These are used as features for pattern classifiers. We considered first two linear classification methods: the Fisher linear discriminant and the linear classifier trained by the Ho-Kayshap algorithm. When the data are not linearly separable, artificial neural networks with back-propagation training and radial basis function networks were then considered, providing nonlinear decision surfaces. Thirdly, a support vector machine was trained which gives tolerance margins on both sides of the decision surface. We have found in this case study that the back-propagation training of an artificial neural network depends heavily on the selection of initial weights, even though randomized. The support vector machine where radial basis function kernels are used is easily trained and provides decision tolerance margins, in spite of only small margins

Beyond the Standard Model with Precision Nucleon Matrix Elements on the Lattice

Precision measurements of nucleons provide constraints on the Standard Model and can discern the signatures predicted for particles beyond the Standard Model (BSM). Knowing the Standard Model inputs to nucleon matrix elements will be necessary to constrain the couplings of dark matter candidates such as the neutralino, to relate the neutron electric dipole moment to the CP-violating theta parameter, or to search for new TeV-scale particles though non-$V-A$ interactions in neutron beta decay. However, these matrix elements derive from the properties of quantum chromodynamics (QCD) at low energies, where perturbative treatments fail. Using lattice gauge theory, we can nonperturbatively calculate the QCD path integral on a supercomputer. In this proceeding, I will discuss a few representative areas in which lattice QCD (LQCD) can contribute to the search for BSM physics, emphasizing suppressed operators in neutron decay, and outline prospects for future development.Comment: 3 pages, 2 figures, talk presented at the 19th Particles and Nuclei International Conference (PANIC 2011), Massachusetts Institute of Technology, Cambridge, MA, USA, July 24-29, 201

Charmed spectroscopy from a nonperturbatively determined relativistic heavy quark action in full QCD

We present a preliminary calculation of the charmed meson spectrum using the 2+1 flavor domain wall fermion lattice configurations currently being generated by the RBC and UKQCD collaborations. The calculation is performed using the 3-parameter, relativistic heavy quark action with nonperturbatively determined coefficients. We will also demonstrate a step-scaling procedure for determining these coefficients nonperturbatively using a series of quenched, gauge field ensembles generated for three different lattice spacings.Comment: Proceeding for 24th International Symposium on Lattice Field Theory (Lattice 2006), Tucson, Arizona, 23-28 Jul 200

Similarity Solutions of a Class of Perturbative Fokker-Planck Equation

In a previous work, a perturbative approach to a class of Fokker-Planck equations, which have constant diffusion coefficients and small time-dependent drift coefficients, was developed by exploiting the close connection between the Fokker-Planck equations and the Schrodinger equations. In this work, we further explore the possibility of similarity solutions of such a class of Fokker-Planck equations. These solutions possess definite scaling behaviors, and are obtained by means of the so-called similarity method

Pointwise Approximation Theorems for Combinations of Bernstein Polynomials With Inner Singularities

We give direct and inverse theorems for the weighted approximation of functions with inner singularities by combinations of Bernstein polynomials.Comment: 13 pages, late