Extensions and degenerations of spectral triples

For a unital C*-algebra A, which is equipped with a spectral triple and an extension T of A by the compacts, we construct a family of spectral triples associated to T and depending on the two positive parameters (s,t). Using Rieffel's notation of quantum Gromov-Hausdorff distance between compact quantum metric spaces it is possible to define a metric on this family of spectral triples, and we show that the distance between a pair of spectral triples varies continuously with respect to the parameters. It turns out that a spectral triple associated to the unitarization of the algebra of compact operators is obtained under the limit - in this metric - for (s,1) -> (0, 1), while the basic spectral triple, associated to A, is obtained from this family under a sort of a dual limiting process for (1, t) -> (1, 0). We show that our constructions will provide families of spectral triples for the unitarized compacts and for the Podles sphere. In the case of the compacts we investigate to which extent our proposed spectral triple satisfies Connes' 7 axioms for noncommutative geometry.Comment: 40 pages. Addedd in ver. 2: Examples for the compacts and the Podle`s sphere plus comments on the relations to matricial quantum metrics. In ver.3 the word "deformations" in the original title has changed to "degenerations" and some illustrative remarks on this aspect are adde

Is there a Jordan geometry underlying quantum physics?

There have been several propositions for a geometric and essentially non-linear formulation of quantum mechanics. From a purely mathematical point of view, the point of view of Jordan algebra theory might give new strength to such approaches: there is a ``Jordan geometry'' belonging to the Jordan part of the algebra of observables, in the same way as Lie groups belong to the Lie part. Both the Lie geometry and the Jordan geometry are well-adapted to describe certain features of quantum theory. We concentrate here on the mathematical description of the Jordan geometry and raise some questions concerning possible relations with foundational issues of quantum theory.Comment: 30 page

Continuity of the Maximum-Entropy Inference

We study the inverse problem of inferring the state of a finite-level quantum system from expected values of a fixed set of observables, by maximizing a continuous ranking function. We have proved earlier that the maximum-entropy inference can be a discontinuous map from the convex set of expected values to the convex set of states because the image contains states of reduced support, while this map restricts to a smooth parametrization of a Gibbsian family of fully supported states. Here we prove for arbitrary ranking functions that the inference is continuous up to boundary points. This follows from a continuity condition in terms of the openness of the restricted linear map from states to their expected values. The openness condition shows also that ranking functions with a discontinuous inference are typical. Moreover it shows that the inference is continuous in the restriction to any polytope which implies that a discontinuity belongs to the quantum domain of non-commutative observables and that a geodesic closure of a Gibbsian family equals the set of maximum-entropy states. We discuss eight descriptions of the set of maximum-entropy states with proofs of accuracy and an analysis of deviations.Comment: 34 pages, 1 figur

Climate policy and ancillary benefits : a survey and integration into the modelling of international negotiations on climate change

Currently informal and formal international negotiations on climate change take place in an intensive way since the Kyoto Protocol expires already in 2012. A post-Kyoto regulation to combat global warming is not yet stipulated. Due to rapidly increasing greenhouse gas emission levels, industrialized countries urge major polluters from the developing world like China and India to participate in a future agreement. Whether these developing countries will do so, depends on the prevailing incentives to participate in international climate protection efforts. This paper identifies ancillary benefits of climate policy to provide important incentives to attend a new international protocol and to positively affect the likelihood of accomplishing a post-Kyoto agreement which includes commitments of developing countries

Semen CD4+ T cells and macrophages are productively infected at all stages of SIV infection in macaques.

International audienceThe mucosal events of HIV transmission have been extensively studied, but the role of infected cells present in the genital and rectal secretions, and in the semen, in particular, remains a matter of debate. As a prerequisite to a thorough in vivo investigation of the early transmission events through infected cells, we characterized in detail by multi-parameter flow cytometry the changes in macaque seminal leukocytes during SIVmac251 infection, focusing on T cells, macrophages and dendritic cells. Using immunocytofluorescence targeting SIV proteins and real-time quantitative PCR targeting SIV DNA, we investigated the nature of the infected cells on sorted semen leukocytes from macaques at different stages of infection. Finally, we cocultured semen CD4(+) T cells and macrophages with a cell line permissive to SIV infection to assess their infectivity in vitro. We found that primary infection induced strong local inflammation, which was associated with an increase in the number of leukocytes in semen, both factors having the potential to favor cell-associated virus transmission. Semen CD4(+) T cells and macrophages were productively infected at all stages of infection and were infectious in vitro. Lymphocytes had a mucosal phenotype and expressed activation (CD69 & HLA-DR) and migration (CCR5, CXCR4, LFA-1) markers. CD69 expression was increased in semen T cells by SIV infection, at all stages of infection. Macrophages predominated at all stages and expressed CD4, CCR5, MAC-1 and LFA-1. Altogether, we demonstrated that semen contains the two major SIV-target cells (CD4+ T cells and macrophages). Both cell types can be productively infected at all stages of SIV infection and are endowed with markers that may facilitate transmission of infection during sexual exposure

Setting the stage: host invasion by HIV.

For more than two decades, HIV has infected millions of people worldwide each year through mucosal transmission. Our knowledge of how HIV secures a foothold at both the molecular and cellular levels has been expanded by recent investigations that have applied new technologies and used improved techniques to isolate ex vivo human tissue and generate in vitro cellular models, as well as more relevant in vivo animal challenge systems. Here, we review the current concepts of the immediate events that follow viral exposure at genital mucosal sites where most documented transmissions occur. Furthermore, we discuss the gaps in our knowledge that are relevant to future studies, which will shape strategies for effective HIV prevention