Compared with Diffusion Tensor Imaging (DTI), High Angular Resolution Imaging (HARDI) can better explore the complex microstructure of white matter. Orientation Distribution Function (ODF) is used to describe the probability of the fiber direction. Fisher information metric has been constructed for probability density family in Information Geometry theory and it has been successfully applied fo...

Many functions on context-free languages can be expressed in the form of the least fixed point of a function whose definition mimics the grammar of the given language. This paper presents the basic theory that explains when a function on a context-free language can be defined in this way. The contributions are: a novel definition of a regular algebra capturing division properties, several theor...

We study certain function algebras and their operator algebra completions on r-discrete abelian groupoids, the corresponding conditional expectations, maximal abelian subalgebras (masa) and eigen-functionals. We give a semidirect product decomposition for an abelian groupoid. This is done through a matched pair and leads to a C*-diagonal (for a special case). We use this decomposition to study ...

This defines an operator MK̄ , which we will call a Minkowski operator. Denote by A(C) the Frechet space of entire functions in n variables with the usual topology of the uniform convergence on compact sets in C, and C(R) the Frechet space of r times differentiable functions on R with the topology of the uniform convergence on compact sets in R of all partial derivatives up to the order r (1 ≤ r...

Regular algebras axiomatise the equational theory of regular expressions as induced by regular language identity. We use Isabelle/HOL for a detailed systematic study of regular algebras given by Boffa, Conway, Kozen and Salomaa. We investigate the relationships between these classes, formalise a soundness proof for the smallest class (Salomaa’s) and obtain completeness of the largest one (Boffa...

For each Dynkin diagram $D$, we define a ''cluster configuration space'' ${\mathcal{M}}_D$ and partial compactification ${\widetilde {\mathcal{M}}}_D$. $D = A_{n-3}$, have ${\mathcal{M}}_{A_{n-3}} {\mathcal{M}}_{0,n}$, the space of $n$ points on ${\mathbb P}^1$, {\mathcal{M}}}_{A_{n-3}}$ was studied in this case by Brown. The {\mathcal{M}}}_D$ is smooth affine algebraic variety with stratificat...

Omega-regular algebras axiomatise the equational theory of omega-regular expressions as induced by omega-regular language identity. Wagner presented an omega-regular algebra which requires recursively defined side conditions in some of its axioms. We introduce a first-order Horn axiomatisation for which such conditions can be avoided because additive and multiplicative units are absent. We prov...

In this paper we study the notions of cogenerator and subdirectlyirreducible in the category of S-poset. First we give somenecessary and sufficient conditions for a cogenerator $S$-posets.Then we see that under some conditions, regular injectivityimplies generator and cogenerator. Recalling Birkhoff'sRepresentation Theorem for algebra, we study subdirectlyirreducible S-posets and give this theo...