This paper proposes a modal extension of Separation Logic [8, 11] for reasoning about data-parallel programs that manipulate heap allocated linked data structures. Separation Logic provides a formal means for expressing allocation of disjoint substructures, which are to be processed in parallel. A modal operator is also introduced to relate the global property of a parallel operation with the l...

Most approaches to the problem of source separation use the assumption of statistical independence. To capture statistical independence higher order statistics are required. In this chapter we will demonstrate how higher order criteria, such as maximum kurtosis, arise naturally from the property of non-stationarity. We will also show that source separation of non-stationary signals can be based...

One of the modern techniques of mixture separation is the application of liquid membranes. They reveal the ability of selective transport of mixture components in which a liquid membrane constitutes a separate phase which separates two other liquid or gas phases. This property of membranes makes them useful in the textile and food industries, in hydrometallurgy, medicine, biotechnology, environ...

We study the shrinking and separation properties (two notions well-known in descriptive set theory) for NP and coNP and show that under reasonable complexity-theoretic assumptions, both properties do not hold for NP and the shrinking property does not hold for coNP. In particular we obtain the following results. 1. NP and coNP do not have the shrinking property, unless PH is finite. In general,...

An important part of training the next generation of physicians is ensuring that they are exposed to the integral role that research plays in improving medical treatment. However, medical students often do not have sufficient time to be trained to carry out any projects in biomedical and clinical research. Many medical students also fail to understand and grasp translational research as an impo...

The λμ-calculus is an extension of the λ-calculus introduced in 1992 by Parigot [17] in order to generalize the Curry-Howard isomorphism to classical logic. Two versions of the calculus are usually considered in the literature: Parigot’s original syntax and an alternative syntax introduced by de Groote. In 2001, David and Py [5] proved that the Separation Property (also referred to as Böhm theo...