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

On the lattice structure of probability spaces in quantum mechanics

Let C be the set of all possible quantum states. We study the convex subsets of C with attention focused on the lattice theoretical structure of these convex subsets and, as a result, find a framework capable of unifying several aspects of quantum mechanics, including entanglement and Jaynes' Max-Ent principle. We also encounter links with entanglement witnesses, which leads to a new separability criteria expressed in lattice language. We also provide an extension of a separability criteria based on convex polytopes to the infinite dimensional case and show that it reveals interesting facets concerning the geometrical structure of the convex subsets. It is seen that the above mentioned framework is also capable of generalization to any statistical theory via the so-called convex operational models' approach. In particular, we show how to extend the geometrical structure underlying entanglement to any statistical model, an extension which may be useful for studying correlations in different generalizations of quantum mechanics.Comment: arXiv admin note: substantial text overlap with arXiv:1008.416

Origin and geochemical evolution of the Madeira-Tore Rise (eastern North Atlantic)

The Madeira-Tore Rise, located ∼700 km off the NW African coast, forms a prominent ridge in the east Atlantic. The age and origin of the rise are controversial. This study presents major and trace element, Sr, Nd, Pb, Hf isotope and 40Ar/39Ar age determinations from volcanic rocks dredged from different sites along the rise. In addition, isotopic compositions of rock samples from Great Meteor Seamount in the central Atlantic are presented. The new radiometric and paleontologically constrained ages identify two major episodes of volcanism: The first is the base of the rise (circa 80 to >95 Ma) and the second is seamounts on the rise (0.5–16 Ma). It is proposed that interaction of the Canary hot spot with the Mid-Atlantic spreading center formed the deep basement of the Madeira-Tore Rise and the J-Anomaly Ridge west of the Atlantic spreading center in the Mid-Cretaceous. Age and geochemical data and plate tectonic reconstructions suggest, however, that the recovered Late Cretaceous volcanic rocks represent late stage volcanism from the time when the Madeira-Tore Rise was still close to the Canary hot spot. Long after moving away from the influence of the Canary hot spot, the Madeira-Tore Rise was overprinted by late Cenozoic volcanism. Miocene to Pleistocene volcanism at the northern end of the rise can be best explained by decompression mantle melting beneath extensional sectors of the Azores-Gibraltar Fracture Zone (African-Eurasian plate boundary). The geochemical compositions of these volcanic rocks suggest that the magmas were variably contaminated by enriched material within or derived by melting of enriched material underplated at the base of the lithosphere, possibly originating from the Cretaceous Canary plume. Alternatively, these late Cenozoic volcanic rocks may have derived from decompression melting of enriched pyroxenitic/eclogitic material in the upper mantle. Isotopically more depleted Pliocene to Pleistocene volcanism at the southern end of the Madeira-Tore Rise may be related to the nearby Madeira hot spot

Pan-cancer analysis of whole genomes

Cancer is driven by genetic change, and the advent of massively parallel sequencing has enabled systematic documentation of this variation at the whole-genome scale(1-3). Here we report the integrative analysis of 2,658 whole-cancer genomes and their matching normal tissues across 38 tumour types from the Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium of the International Cancer Genome Consortium (ICGC) and The Cancer Genome Atlas (TCGA). We describe the generation of the PCAWG resource, facilitated by international data sharing using compute clouds. On average, cancer genomes contained 4-5 driver mutations when combining coding and non-coding genomic elements; however, in around 5% of cases no drivers were identified, suggesting that cancer driver discovery is not yet complete. Chromothripsis, in which many clustered structural variants arise in a single catastrophic event, is frequently an early event in tumour evolution; in acral melanoma, for example, these events precede most somatic point mutations and affect several cancer-associated genes simultaneously. Cancers with abnormal telomere maintenance often originate from tissues with low replicative activity and show several mechanisms of preventing telomere attrition to critical levels. Common and rare germline variants affect patterns of somatic mutation, including point mutations, structural variants and somatic retrotransposition. A collection of papers from the PCAWG Consortium describes non-coding mutations that drive cancer beyond those in the TERT promoter(4); identifies new signatures of mutational processes that cause base substitutions, small insertions and deletions and structural variation(5,6); analyses timings and patterns of tumour evolution(7); describes the diverse transcriptional consequences of somatic mutation on splicing, expression levels, fusion genes and promoter activity(8,9); and evaluates a range of more-specialized features of cancer genomes(8,10-18).Peer reviewe

Comprehensive analysis of chromothripsis in 2,658 human cancers using whole-genome sequencing

Chromothripsis is a mutational phenomenon characterized by massive, clustered genomic rearrangements that occurs in cancer and other diseases. Recent studies in selected cancer types have suggested that chromothripsis may be more common than initially inferred from low-resolution copy-number data. Here, as part of the Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium of the International Cancer Genome Consortium (ICGC) and The Cancer Genome Atlas (TCGA), we analyze patterns of chromothripsis across 2,658 tumors from 38 cancer types using whole-genome sequencing data. We find that chromothripsis events are pervasive across cancers, with a frequency of more than 50% in several cancer types. Whereas canonical chromothripsis profiles display oscillations between two copy-number states, a considerable fraction of events involve multiple chromosomes and additional structural alterations. In addition to non-homologous end joining, we detect signatures of replication-associated processes and templated insertions. Chromothripsis contributes to oncogene amplification and to inactivation of genes such as mismatch-repair-related genes. These findings show that chromothripsis is a major process that drives genome evolution in human cancer