Fuzzy Least Squares Twin Support Vector Machines

Least Squares Twin Support Vector Machine (LST-SVM) has been shown to be an efficient and fast algorithm for binary classification. It combines the operating principles of Least Squares SVM (LS-SVM) and Twin SVM (T-SVM); it constructs two non-parallel hyperplanes (as in T-SVM) by solving two systems of linear equations (as in LS-SVM). Despite its efficiency, LST-SVM is still unable to cope with two features of real-world problems. First, in many real-world applications, labels of samples are not deterministic; they come naturally with their associated membership degrees. Second, samples in real-world applications may not be equally important and their importance degrees affect the classification. In this paper, we propose Fuzzy LST-SVM (FLST-SVM) to deal with these two characteristics of real-world data. Two models are introduced for FLST-SVM: the first model builds up crisp hyperplanes using training samples and their corresponding membership degrees. The second model, on the other hand, constructs fuzzy hyperplanes using training samples and their membership degrees. Numerical evaluation of the proposed method with synthetic and real datasets demonstrate significant improvement in the classification accuracy of FLST-SVM when compared to well-known existing versions of SVM

Neural Dynamics of Motion Processing and Speed Discrimination

A neural network model of visual motion perception and speed discrimination is presented. The model shows how a distributed population code of speed tuning, that realizes a size-speed correlation, can be derived from the simplest mechanisms whereby activations of multiple spatially short-range filters of different size are transformed into speed-tuned cell responses. These mechanisms use transient cell responses to moving stimuli, output thresholds that covary with filter size, and competition. These mechanisms are proposed to occur in the Vl→7 MT cortical processing stream. The model reproduces empirically derived speed discrimination curves and simulates data showing how visual speed perception and discrimination can be affected by stimulus contrast, duration, dot density and spatial frequency. Model motion mechanisms are analogous to mechanisms that have been used to model 3-D form and figure-ground perception. The model forms the front end of a larger motion processing system that has been used to simulate how global motion capture occurs, and how spatial attention is drawn to moving forms. It provides a computational foundation for an emerging neural theory of 3-D form and motion perception.Office of Naval Research (N00014-92-J-4015, N00014-91-J-4100, N00014-95-1-0657, N00014-95-1-0409, N00014-94-1-0597, N00014-95-1-0409); Air Force Office of Scientific Research (F49620-92-J-0499); National Science Foundation (IRI-90-00530

Analysis of the pion-kaon sigma-term and related topics

We calculate the one-loop contributions to the difference \Delta_{\pi K} between the isoscalar on-shell pion-kaon scattering amplitude at the Cheng-Dashen point and the scalar form factor \Gamma_K (2M_\pi^2) in the framework of three flavor chiral perturbation theory. These corrections turn out to be small. This is further sharpened by treating the kaons as heavy fields (two flavor chiral perturbation theory). We also analyze the two-loop corrections to the kaon scalar form factor based on a dispersive technique. We find that these corrections are smaller than in the comparable case of the scalar form factor of the pion. This is related to the weaker final state interactions in the pion-kaon channel.Comment: 25 pp, 3 fig

SU(2)xSU(2) Invariant Scattering Matrix of the Hubbard Model

We consider the one-dimensional half-filled Hubbard model. We show that the excitation spectrum is given by the scattering states of four elementary excitations, which form the fundamental representation of $SU(2)\times SU(2)$. We determine the exact two-particle Scattering matrix, which a solution of the Yang-Baxter equation and reflects the $SO(4)$ symmetry of the model. The results for repulsive and attractive Hubbard model are related by an interchange of spin and charge degrees of freedom.Comment: 29 pages, jyTeX (macro included - just TeX the file) ITP-SB-93-45, BONN-HE-93-3

CAMORRA: a C++ library for recursive computation of particle scattering amplitudes

We present a new Monte Carlo tool that computes full tree-level matrix elements in high-energy physics. The program accepts user-defined models and has no restrictions on the process multiplicity. To achieve acceptable performance, CAMORRA evaluates the matrix elements in a recursive way by combining off-shell currents. Furthermore, CAMORRA can be used to compute amplitudes involving continuous color and helicity final states.Comment: 22 page

Dynamics on Grassmannians and resolvents of cone operators

The paper proves the existence and elucidates the structure of the asymptotic expansion of the trace of the resolvent of a closed extension of a general elliptic cone operator on a compact manifold with boundary as the spectral parameter tends to infinity. The hypotheses involve only minimal conditions on the symbols of the operator. The results combine previous investigations by the authors on the subject with an analysis of the asymptotics of a family of projections related to the domain. This entails a fairly detailed study of the dynamics of a flow on the Grassmannian of domains.Comment: 34 page