Logical systems with classical negation and means for sentential or propositional self-reference involve, in some way, paradoxical statements such as the liar. However, the paradox disappears if one replaces classical by an appropriate non-classical negation such as a paraconsistent one (no paradox arises if the liar is both true and false). We consider a non-Fregean logic which is a revised an...

This paper briefly describes a framework for storage of geometric tensor array data, useful for storage of regularly sampled tensor fields and regularly sampled tensor-valued functions on charts of manifolds in differential geometry. The framework, called Similar Tensor Array Core Headers, abbreviated STACH and pronounced like the english word ”stash”, capture the essence of tensor field proces...

A quantization scheme for the phenomenological Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive and absorbing dielectric medium is developed. The classical Maxwell equations with spatially varying and Kramers–Kronig consistent permittivity are regarded as operator-valued field equations, introducing additional currentand charge-density operator ...

Starting from essentially commutative exponential map E(B|I) for generic tensor-valued 2-forms B, introduced in [1] as direct generalization of the ordinary non-commutative P -exponent for 1-forms with values in matrices (i.e. in tensors of rank 2), we suggest a non-trivial but multi-parametric exponential E(B|I|tγ), which can serve as an interesting multi-directional evolution operator in the ...

We derive a Hodge decomposition of discrete vector fields on polyhedral surfaces, and apply it to the identification of vector field singularities. This novel approach allows us to easily detect and analyze singularities as critical points of corresponding potentials. Our method uses a global variational approach to independently compute two potentials whose gradient respectively co-gradient ar...

We define and derive some properties of the different multiple view tensors. The multiple view geometry is described using a four-dimensional linear manifold in IR3m, wherem denotes the number of images. The Grassman coordinates of this manifold build up the components of the different multiple view tensors. All relations between these Grassman coordinates can be expressed using the quadratic p...

Second-order tensors may be described in terms of shape and orientation. Shape is quantified by tensor invariants, which are fixed with respect to coordinate system changes. This chapter describes an anatomically-motivated method of detecting edges in diffusion tensor fields based on the gradients of invariants. Three particular invariants (the mean, variance, and skewness of the tensor eigenva...

The generalized Killing equations for the configuration space of spinning particles (spinning space) are analysed. Solutions of these equations are expressed in terms of Killing-Yano tensors. In general the constants of motion can be seen as extensions of those from the scalar case or new ones depending on the Grassmann-valued spin variables. Spinning particles, such as Dirac fermions, can be d...

In many image analysis applications there is a need to extract curves in noisy images. To achieve a more robust extraction, one can exploit correlations of oriented features over a spatial context in the image. Tensor voting is an existing technique to extract features in this way. In this paper, we present a new computational scheme for tensor voting on a dense field of rank-2 tensors. Using s...

In this work we propose a generalization of the Hadamard product between two matrices to a tensor-valued, multi-linear product between k matrices for any k ≥ 1. A multi-linear dual operator to the generalized Hadamard product is presented. It is a natural generalization of the Diag x operator, that maps a vector x ∈ R into the diagonal matrix with x on its main diagonal. Defining an action of t...