The structure of classical extensions of quantum probability theory

On the basis of a suggestive definition of a classical extension of quantum mechanics in terms of statistical models, we prove that every such classical extension is essentially given by the so-called Misra–Bugajski reduction map. We consider how this map enables one to understand quantum mechanics as a reduced classical statistical theory on the projective Hilbert space as phase space and discuss features of the induced hidden-variable model. Moreover, some relevant technical results on the topology and Borel structure of the projective Hilbert space are reviewed

New Avoparcin-like Molecules from the Avoparcin Producer Amycolatopsis coloradensis ATCC 53629

Amycolatopsis coloradensis ATCC 53629 is the producer of the glycopeptide antibiotic avoparcin. While setting up the production of the avoparcin complex, in view of its use as analytical standard, we uncovered the production of a to-date not described ristosamynil-avoparcin. Ristosamynil-avoparcin is produced together with α-and β-avoparcin (overall indicated as the avoparcin complex). Selection of one high producer morphological variant within the A. coloradensis population, together with the use of a new fermentation medium, allowed to increase productivity of the avoparcin complex up to 9 g/L in flask fermentations. The selected high producer displayed a non-spore forming phenotype. All the selected phenotypes, as well as the original unselected population, displayed invariably the ability to produce a complex rich in ristosamynil-avoparcin. This suggested that the original strain deposited was not conforming to the description or that long term storage of the lyovials has selected mutants from the original population

Connectivity and a Problem of Formal Geometry

Let $P=\mathbb P^m(e)\times\mathbb P^n(h)$ be a product of weighted projective spaces, and let $\Delta_P$ be the diagonal of $P\times P$. We prove an algebraization result for formal-rational functions on certain closed subvarieties $X$ of $P\times P$ along the intersection $X\cap\Delta_P$.Comment: 9 pages, to appear in the Proceedings volume "Experimental and Theoretical Methods in Algebra, Geometry and Topology", series Springer Proceedings in Mathematics & Statistic

Informing additive manufacturing technology adoption: total cost and the impact of capacity utilisation

Informing Additive Manufacturing (AM) technology adoption decisions, this paper investigates the relationship between build volume capacity utilisation and efficient technology operation in an inter-process comparison of the costs of manufacturing a complex component used in the packaging industry. Confronting the reported costs of a conventional machining and welding pathway with an estimator of the costs incurred through an AM route utilising Direct Metal Laser Sintering (DMLS), we weave together four aspects: optimised capacity utilisation, ancillary process steps, the effect of build failure and design adaptation. Recognising that AM users can fill unused machine capacity with other, potentially unrelated, geometries, we posit a characteristic of ‘fungible’ build capacity. This aspect is integrated in the cost estimation framework through computational build volume packing, drawing on a basket of sample geometries. We show that the unit cost in mixed builds at full capacity is lower than in builds limited to a single type of geometry; in our study, this results in a mean unit cost overstatement of 157%. The estimated manufacturing cost savings from AM adoption range from 36 to 46%. Additionally, we indicate that operating cost savings resulting from design adaptation are likely to far outweigh the manufacturing cost advantage

Classical statistical distributions can violate Bell-type inequalities

We investigate two-particle phase-space distributions in classical mechanics characterized by a well-defined value of the total angular momentum. We construct phase-space averages of observables related to the projection of the particles' angular momenta along axes with different orientations. It is shown that for certain observables, the correlation function violates Bell's inequality. The key to the violation resides in choosing observables impeding the realization of the counterfactual event that plays a prominent role in the derivation of the inequalities. This situation can have statistical (detection related) or dynamical (interaction related) underpinnings, but non-locality does not play any role.Comment: v3: Extended version. To be published in J. Phys.

Linear Toric Fibrations

These notes are based on three lectures given at the 2013 CIME/CIRM summer school. The purpose of this series of lectures is to introduce the notion of a toric fibration and to give its geometrical and combinatorial characterizations. Polarized toric varieties which are birationally equivalent to projective toric bundles are associated to a class of polytopes called Cayley polytopes. Their geometry and combinatorics have a fruitful interplay leading to fundamental insight in both directions. These notes will illustrate geometrical phenomena, in algebraic geometry and neighboring fields, which are characterized by a Cayley structure. Examples are projective duality of toric varieties and polyhedral adjunction theory

A quantum logical and geometrical approach to the study of improper mixtures

We study improper mixtures from a quantum logical and geometrical point of view. Taking into account the fact that improper mixtures do not admit an ignorance interpretation and must be considered as states in their own right, we do not follow the standard approach which considers improper mixtures as measures over the algebra of projections. Instead of it, we use the convex set of states in order to construct a new lattice whose atoms are all physical states: pure states and improper mixtures. This is done in order to overcome one of the problems which appear in the standard quantum logical formalism, namely, that for a subsystem of a larger system in an entangled state, the conjunction of all actual properties of the subsystem does not yield its actual state. In fact, its state is an improper mixture and cannot be represented in the von Neumann lattice as a minimal property which determines all other properties as is the case for pure states or classical systems. The new lattice also contains all propositions of the von Neumann lattice. We argue that this extension expresses in an algebraic form the fact that -alike the classical case- quantum interactions produce non trivial correlations between the systems. Finally, we study the maps which can be defined between the extended lattice of a compound system and the lattices of its subsystems.Comment: submitted to the Journal of Mathematical Physic