Major advances in medical imaging raised the need for adapted methods and softwares. The recent emergence of diffusion tensor MRI (DT-MRI) was challenging since data produced by this modality are not simple grey-value images but complex diffusion tensor fields. Tensors are symmetric, positive definite matrices and suffer from a lack of adapted theoretical tools to manipulate them. In this paper...

We present the properties of new Dirac-type operators generated by real or complex-valued special Killing-Yano tensors that are covariantly constant and represent roots of the metric tensor. In the real case these are just the so called complex or hyper-complex structures of the Kählerian manifolds. Such a Killing-Yano tensor produces simultaneously a Dirac-type operator and the generator of a ...

We present a Bayesian non-negative tensor factorization model for count-valued tensor data, and develop scalable inference algorithms (both batch and online) for dealing with massive tensors. Our generative model can handle overdispersed counts as well as infer the rank of the decomposition. Moreover, leveraging a reparameterization of the Poisson distribution as a multinomial facilitates conju...

This paper describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the socalled Minkowski tensors. Minkowski tensors are generalizations of the wellknown scalar Minkowski functionals and are explicitly sensitive to anisotropic aspects of morphology, relevant...

The aim of this chapter is to review different approaches that have been proposed to compute fabric tensors with emphasis on trabecular bone research. Fabric tensors aim at modeling through tensors both anisotropy and orientation of a material with respect to another one. Fabric tensors are widely used in fields such as trabecular bone research, mechanics of materials and geology. These tensors...

This paper presents an experiment with human subjects concerning the vague spatial relation ‘near’ in environmental space. After the topic is introduced and relevant previous work surveyed, the experiment is described. Three approaches to experimental analysis are presented and discussed: nearness neighbourhoods as regions with broad boundaries, fuzzy nearness and distance measures, and four-va...

We consider the curvatures 2 form asociated with AdSL4 valued one-form gauge connetion, and then we construct a four-dimensional action that generalize Einstein-Hilbert gravity. It is shown Maxwell extension of Einstein gravity can be obtained from AdSL4-gravity making use Inonu-Wigner contraction method. In same way, by gauging AdSL5 spacetime algebra, extended including vector fields kab ha w...

Kleene’s strong three-valued logic extends naturally to a four-valued logic proposed by Belnap. We introduce a guard connective into Belnap’s logic and consider a few of its properties. Then we show that by using it four-valued analogs of Kleene’s weak three-valued logic, and the asymmetric logic of Lisp are also available. We propose an extension of these ideas to the family of distributive bi...

1 Tensors Tensors are the generalizations of vectors v ∈ R and matrices M ∈ Rm×n. These are respectively 1-tensors and 2-tensors, which we can represent using oneand two-dimensional arrays of real numbers. Although there are more general definitions, for our purposes, a p-th order tensor (or a p-tensor) is an object that can be represented using a p-dimensional array of real numbers. Technicall...