The paper studies stochastic integration with respect to Gaussian processes and fields. It is more convenient to work with a field than a process: by definition, a field is a collection of stochastic integrals for a class of deterministic integrands. The problem is then to extend the definition to random integrands. An orthogonal decomposition of chaos space of the random field leads to two suc...

We provide a geometrical identification of the ghost fields, essential to the renormalization procedure in the non-Abelian (Yang-Mills) case. These are some of the local components of a connection on a principal bundle. They multiply the differentials of coordinates spanning directions orthogonal to those of a given section, whereas the Yang-Mills potential multiplies the coordinates in the sec...

Abstract: We obtain formulae for the expected number and height distribution of critical points of general smooth isotropic Gaussian random fields parameterized on Euclidean space or spheres of arbitrary dimension. The results hold in general in the sense that there are no restrictions on the covariance function of the field except for smoothness and isotropy. The results are based on a charact...

This paper concerns the estimation of apparent motion from an image sequence. A model, named full model, is defined to describe the dynamics of motion field and images. The Proper Orthogonal Decomposition (POD) is used to derive basis to characterize motion fields and images. The Galerkin projection of the full model on these basis defines the so-called reduced model. Coefficients of motion fie...

The b = √ 3 RGT [1] has a number of advantages compared to b = 2 [2,3]: it 1) has a smaller step size, 2) incorporates more gluonic degrees of freedom, 3) requires less tuning parameters, 4) has no overlap of either gauge or fermion fields between neighboring block cells, and 5) preserves a higher rotational symmetry for matter fields. This work complements the previous estimate of the renormal...

We present a method for detecting and describing features in vector flow fields. Our method models flow fields locally using a linear combination of complex monomials. These monomials form an orthogonal basis for analytic flows with respect to a correlation-based innerproduct. We investigate the invariance properties of the coefficients of the approximation polynomials under both rotation and s...

We consider a 5-dimensional scalar-tensor theory which is a direct generalization of the original 4-dimensional Brans-Dicke theory to 5-dimensions. By assuming that there is a hypersurface-orthogonal spacelike Killing vector field in the underlying 5-dimensional spacetime, the theory is reduced to a 4-dimensional theory where the 4-metric is coupled with two scalar fields. The cosmological impl...

A parametric manifold is a manifold on which all tensor fields depend on an additional parameter, such as time, together with a parametric structure, namely a given (parametric) 1-form field. Such a manifold admits natural generalizations of Lie differentiation, exterior differentiation, and covariant differentiation, all based on a nonstandard action of vector fields on functions. There is a n...

To examine the role of primary visual cortex in visuospatial integration, we studied the spatial arrangement of contextual interactions in the response properties of neurons in primary visual cortex of alert monkeys and in human perception. We found a spatial segregation of opposing contextual interactions. At the level of cortical neurons, excitatory interactions were located along the ends of...