Quantum symmetries for exceptional SU(4) modular invariants associated with conformal embeddings

Three exceptional modular invariants of SU(4) exist at levels 4, 6 and 8. They can be obtained from appropriate conformal embeddings and the corresponding graphs have self-fusion. From these embeddings, or from their associated modular invariants, we determine the algebras of quantum symmetries, obtain their generators,and, as a by-product, recover the known graphs E4, E6 and E8 describing exceptional quantum subgroups of type SU(4). We also obtain characteristic numbers (quantum cardinalities, dimensions) for each of them and for their associated quantum groupoïds.

A model structure for coloured operads in symmetric spectra

We describe a model structure for coloured operads with values in the category of symmetric spectra (with the positive model structure), in which fibrations and weak equivalences are defined at the level of the underlying collections. This allows us to treat R-module spectra (where R is a cofibrant ring spectrum) as algebras over a cofibrant spectrum-valued operad with R as its first term. Using this model structure, we give sufficient conditions for homotopical localizations in the category of symmetric spectra to preserve module structures.

Equivariant semiprojectivity

We define equivariant semiprojectivity for C* -algebras equipped with actions of compact groups. We prove that the following examples are equivariantly semiprojective: A. Arbitrary finite dimensional C*-algebras with arbitrary actions of compact groups. - B. The Cuntz algebras Od and extended Cuntz algebras Ed, for finite d, with quasifree actions of compact groups. - C. The Cuntz algebra O∞ with any quasifree action of a finite group. For actions of finite groups, we prove that equivariant semiprojectivity is equiv- alent to a form of equivariant stability of generators and relations. We also prove that if G is finite, then C*(G) is graded semiprojective.

Space-time within general relativity : a structural realist understanding

ABSTRACT This dissertation investigates the, nature of space-time as described by the theory of general relativity. It mainly argues that space-time can be naturally interpreted as a physical structure in the precise sense of a network of concrete space-time relations among concrete space-time points that do not possess any intrinsic properties and any intrinsic identity. Such an interpretation is fundamentally based on two related key features of general relativity, namely substantive general covariance and background independence, where substantive general covariance is understood as a gauge-theoretic invariance under active diffeomorphisms and background independence is understood in the sense that the metric (or gravitational) field is dynamical and that, strictly speaking, it cannot be uniquely split into a purely gravitational part and a fixed purely inertial part or background. More broadly, a precise notion of (physical) structure is developed within the framework of a moderate version of structural realism understood as a metaphysical claim about what there is in the world. So, the developement of this moderate structural realism pursues two main aims. The first is purely metaphysical, the aim being to develop a coherent metaphysics of structures and of objects (particular attention is paid to the questions of identity and individuality of these latter within this structural realist framework). The second is to argue that moderate structural realism provides a convincing interpretation of the world as described by fundamental physics and in particular of space-time as described by general relativity. This structuralist interpretation of space-time is discussed within the traditional substantivalist-relationalist debate, which is best understood within the broader framework of the question about the relationship between space-time on the one hand and matter on the other. In particular, it is claimed that space-time structuralism does not constitute a 'tertium quid' in the traditional debate. Some new light on the question of the nature of space-time may be shed from the fundamental foundational issue of space-time singularities. Their possible 'non-local' (or global) feature is discussed in some detail and it is argued that a broad structuralist conception of space-time may provide a physically meaningful understanding of space-time singularities, which is not plagued by the conceptual difficulties of the usual atomsitic framework. Indeed, part of these difficulties may come from the standard differential geometric description of space-time, which encodes to some extent this atomistic framework; it raises the question of the importance of the mathematical formalism for the interpretation of space-time.

Multicenter, Prospective Clinical Evaluation of Respiratory Samples from Subjects at Risk for Pneumocystis jirovecii Infection by Use of a Commercial Real-Time PCR Assay.

Pneumocystis jirovecii pneumonia (PCP) is a common opportunistic infection. Microscopic diagnosis, including diagnosis using the Merifluor-Pneumocystis direct fluorescent antigen (MP-DFA) test, has limitations. Real-time PCR may assist in diagnosis, but no commercially validated real-time PCR assay has been available to date. MycAssay Pneumocystis is a commercial assay that targets the P. jirovecii mitochondrial large subunit (analytical detection limit, ≤3.5 copies/μl of sample). A multicenter trial recruited 110 subjects: 54 with transplants (40 with lung transplants), 32 with nonmalignant conditions, 13 with leukemia, and 11 with solid tumors; 9 were HIV positive. A total of 110 respiratory samples (92% of which were bronchoalveolar lavage [BAL] specimens) were analyzed by PCR. Performance was characterized relative to investigator-determined clinical diagnosis of PCP (including local diagnostic tests), and PCR results were compared with MP-DFA test results for 83 subjects. Thirteen of 14 subjects with PCP and 9/96 without PCP (including 5 undergoing BAL surveillance after lung transplantation) had positive PCR results; sensitivity, specificity, and positive and negative predictive values (PPV and NPV, respectively) were 93%, 91%, 59%, and 99%, respectively. Fourteen of 83 subjects for whom PCR and MP-DFA test results were available had PCP; PCR sensitivity, specificity, PPV, and NPV were 93%, 90%, 65%, and 98%, respectively, and MP-DFA test sensitivity, specificity, PPV, and NPV were 93%, 100%, 100%, and 98%. Of the 9 PCR-positive subjects without PCP, 1 later developed PCP. The PCR diagnostic assay compares well with clinical diagnosis using nonmolecular methods. Additional positive results compared with the MP-DFA test may reflect low-level infection or colonization.

Graded algebra automorphisms

We consider the Clifford algebra C(q) of a regular quadratic space (V, q) over a field K with its structure of Z/2Z-graded K-algebra. We give a characterization of the group of graded automorphisms of C(q). In the last section we introduce the Z/nZ-graded algebras and we study as well as the group of graded automorphisms for some of them.

Poincaré is a subgroup of Galilei in one space dimension more

Through an imaginary change of coordinates, the ordinary Poincar algebra is shown to be a subalgebra of the Galilei one in four space dimensions. Through a subsequent contraction the remaining Lie generators are eliminated in a natural way. An application of these results to connect Galilean and relativistic field equations is discussed.

General Interaction Picture from Action Principle for Mechanics

In this paper we consider a general action principle for mechanics written by means of the elements of a Lie algebra. We study the physical reasons why we have to choose precisely a Lie algebra to write the action principle. By means of such an action principle we work out the equations of motion and a technique to evaluate perturbations in a general mechanics that is equivalent to a general interaction picture. Classical or quantum mechanics come out as particular cases when we make realizations of the Lie algebra by derivations into the algebra of products of functions or operators, respectively. Later on we develop in particular the applications of the action principle to classical and quantum mechanics, seeing that in this last case it agrees with Schwinger's action principle. The main contribution of this paper is to introduce a perturbation theory and an interaction picture of classical mechanics on the same footing as in quantum mechanics.

Collineations of a symmetric 2-covariant tensor: Ricci collineations

The infinitesimal transformations that leave invariant a two-covariant symmetric tensor are studied. The interest of these symmetry transformations lays in the fact that this class of tensors includes the energy-momentum and Ricci tensors. We find that in most cases the class of infinitesimal generators of these transformations is a finite dimensional Lie algebra, but in some cases exhibiting a higher degree of degeneracy, this class is infinite dimensional and may fail to be a Lie algebra. As an application, we study the Ricci collineations of a type B warped spacetime.

Intrinsic subspace convergence in TDD MIMO communication

In numerical linear algebra, students encounter earlythe iterative power method, which finds eigenvectors of a matrixfrom an arbitrary starting point through repeated normalizationand multiplications by the matrix itself. In practice, more sophisticatedmethods are used nowadays, threatening to make the powermethod a historical and pedagogic footnote. However, in the contextof communication over a time-division duplex (TDD) multipleinputmultiple-output (MIMO) channel, the power method takes aspecial position. It can be viewed as an intrinsic part of the uplinkand downlink communication switching, enabling estimationof the eigenmodes of the channel without extra overhead. Generalizingthe method to vector subspaces, communication in thesubspaces with the best receive and transmit signal-to-noise ratio(SNR) is made possible. In exploring this intrinsic subspace convergence(ISC), we show that several published and new schemes canbe cast into a common framework where all members benefit fromthe ISC.