The classical theory of statistical signal extraction presupposes lengthy data sequences, which are assumed, in theory, to be doubly infinite or semi-infinite— see Whittle (1983), for example. In many practical cases, and in most econometric applications, the available data are, to the contrary, both strongly trended and of a limited duration. This paper is concerned with the theory of finite-s...

In 2002 Coecke and Martin created a Bayesian order for the finite dimensional spaces of classical states in physics and used this to define a similar order, the spectral order on the finite dimensional quantum states. These orders gave the spaces a structure similar to that of a domain. This allows for measuring information content of states and for determining which partial states are approxim...

Extending work of Puninski, Puninskaya and Toffalori in [PPT07], we show that if V is an effectively given valuation domain then the theory of all V -modules is decidable if and only if there exists an algorithm which, given a, b ∈ V , answers whether a ∈ rad(bV ). This was conjectured in [PPT07] for valuation domains with dense value group where it was proved for valuation domains with dense a...

We endow the collection of ω-bifinite domains with the structure of a probability space, and we will show that in this space the collection of all universal domains has measure 1. For this, we present a probabilistic way to extend a finite partial order by one element. Applying this procedure iteratively, we obtain an infinite partial order. We show that, with probability 1, the cpo-completion ...

A novel straightforward, accessible and efficient approach is presented for performing hyperspectral time-domain diffuse optical spectroscopy to determine the optical properties of samples accurately using geometry specific models. To allow bulk parameter recovery from measured spectra, a set of libraries based on a numerical model of the domain being investigated is developed as opposed to the...

The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but neither temperature nor heat flux is prescribed there. Instead, the physical assumptions of their continuity at the interfaces are the only conditions imposed. T...