Separability of signal mixtures given only one mixture observation is defined as the identification of the accuracy to which the signals can be separated. The paper shows that when signals are separated using the generalised Wiener filter, the degree of separability can be deduced from the filter structure. To identify this structure, the processes are represented on an arbitrary spectral domai...

We present an elementary and explicit proof of the separability criterion for continuous variable two-party Gaussian systems. Our proof is based on an elementary formulation of uncertainty relations and an explicit determination of squeezing parameters for which the P-representation condition saturates the Sp(2, R) ⊗ Sp(2, R) invariant separability condition. We thus give the explicit formulas ...

Formal models of categorization make different predictions about the theoretical importance of linear separability. Prior research, most of which has failed to find support for a linear separability constraint on category learning, has been conducted using tasks that involve learning two categories with a small number of members. The present experiment used four categories with three or nine pa...

Despite conceptual and technology advancements in cartography over the decades, choropleth map design and classification fail to address a fundamental issue: estimates that are statistically indifferent may be assigned to different classes on maps or vice versa. Recently, the class separability concept was introduced as a map classification criterion to evaluate the likelihood that estimates in...

In the present paper the cross norm criterion for separability of density matrices is studied. In the first part of the paper we determine the value of the greatest cross norm for Werner states, for isotropic states and for Bell diagonal states. In the second part we show that the greatest cross norm criterion induces a novel computable separability criterion for bipartite systems. This new cri...

Hyperspectral data potentially contain more information than multispectral data because of their higher spectral resolution. However, the stochastic data analysis approaches, successfully applied to classification of multispectral data, are not as effective as those for hyperspectral data. Various investigations indicate that the key problem causing poor performance in the stochastic approaches...

The remarkable and unexpected separability of the Hamilton-Jacobi and Klein-Gordon equations in the background of a rotating four-dimensional black hole played an important rôle in the construction of generalisations of the Kerr metric, and in the uncovering of hidden symmetries associated with the existence of Killing tensors. In this paper, we show that the Hamilton-Jacobi and Klein-Gordon eq...

We consider the problem of allocating an infinitely divisible commodity among a group of agents with single-peaked preferences. A rule that has played a central role in the analysis of the problem is the so-called uniform rule. Chun (2001) proves that the uniform rule is the only rule satisfying Pareto optimality, no-envy, separability, and -continuity. We obtain an alternative characterization...

Cumulative Prospect Theory of Tversky and Kahneman (1992) is the modern version of Prospect Theory (Kahneman and Tversky (1979)) and is nowadays considered a valid alternative to the classical Expected Utility Theory. Cumulative Prospect theory implies Gain-Loss Separability, i.e. the separate evaluation of losses and gains within a mixed gamble. Recently, some authors have questioned this assu...

The nonseparability of physical systems is often invoked in philosophical analyses of what has come to be known as Bell’s Theorem. Until recently, the formalization of the notion of separability was assumed to be unproblematic, equivalent to that of outcome independence (Jarrett incompleteness). Although this equivalence has been called into question, an alternative has not yet been specified w...