Notions of Infinity in Quantum Physics

In this article we will review some notions of infiniteness that appear in Hilbert space operators and operator algebras. These include proper infiniteness, Murray von Neumann's classification into type I and type III factors and the class of F{/o} lner C*-algebras that capture some aspects of amenability. We will also mention how these notions reappear in the description of certain mathematical aspects of quantum mechanics, quantum field theory and the theory of superselection sectors. We also show that the algebra of the canonical anti-commutation relations (CAR-algebra) is in the class of F{/o} lner C*-algebras.Comment: 11 page

Twisted duality of the CAR-Algebra

We give a complete proof of the twisted duality property M(q)'= Z M(q^\perp) Z* of the (self-dual) CAR-Algebra in any Fock representation. The proof is based on the natural Halmos decomposition of the (reference) Hilbert space when two suitable closed subspaces have been distinguished. We use modular theory and techniques developed by Kato concerning pairs of projections in some essential steps of the proof. As a byproduct of the proof we obtain an explicit and simple formula for the graph of the modular operator. This formula can be also applied to fermionic free nets, hence giving a formula of the modular operator for any double cone.Comment: 32 pages, Latex2e, to appear in Journal of Mathematical Physic

Quantum twistors

We compute explicitly a star product on the Minkowski space whose Poisson bracket is quadratic. This star product corresponds to a deformation of the conformal spacetime, whose big cell is the Minkowski spacetime. The description of Minkowski space is made in the twistor formalism and the quantization follows by substituting the classical conformal group by a quantum group.Comment: 47 pages. references added, some parts rewritten. To appear in 'p-adic Numbers, Ultrametric Analysis and Applicarions

Molecular phylogenetics of Limonium and related genera (Plumbaginaceae): biogeographical and systematic implications

Phylogenetic relationships within Limonium (Plumbaginaceae) are evaluated using sequence data from three plastid regions (rbcL, the trnL intron, and the trnL-trnF intergenic spacer). Sixty-six species representing the major genera of Staticoideae, including representatives of all sections and genera formerly included in Limonium, have been analyzed using four species of Plumbaginoideae as an outgroup. Analyses of each separate and combined data set yield similar results. Afrolimon is embedded in Limonium and related to L. vulgare, the type of Limonium. Limonium is split into two major clades corresponding to subgenera, but otherwise the current infrageneric classification proved to be artificial. Some groups restricted to particular areas can be recognized, and their synapomorphies are discussed. The presence of an isolated taxon in the Canary Islands is used as a calibration point for age estimates of the major events in the genus, including migrations to the Southern Hemisphere, the Canary Islands, and Asia. The rapid radiation of Limonium in the Mediterranean basin appears to coincide with the desiccation of the Mediterranean Sea in the Messinian (late Miocene).Funding for this project was provided by the Royal Botanic Gardens, Kew, and Consellería de Educación y Ciencia (Comunidad Valenciana, Spain)

Desenvolvimento de hábitos saudáveis no ensino fundamental

Resumen: Introducción: Hoy en día ha aumentado la tasa de sobrepeso, al igual que también se ha visto afectado la disminución de la práctica de deportes y un desconocimiento por lo que se está comiendo. De este modo, desde la Educación física, conjuntamente con el resto de materias, hay que trabajar para que los escolares adquieran buenos hábitos saludables mediante una manera poco convencional, como es hacerlo a través de una gymkhana. Objetivos: Desarrollar los buenos hábitos en alumnos de primaria y aprender de forma lúdica y amena. Métodos: A través de una sesión de Educación física. Resultados y discusión: Tras realizar la sesión, se pretende que los alumnos hayan aprendido unos hábitos saludables mediante una gymkhana. Conclusiones: Concienciar a los alumnos de que adquieran buenos hábitos, puesto que tiene efectos positivos en los ámbitos personales, emocionales y académicos, y que se puede aprender de forma diferente como puede ser a través de la gymkhana.Abstract: Introduction: Nowadays, the rate of overweight in children has increased, as well as the decrease in sports and a lack of knowledge about what is being eaten. Thus, from Physical Education, together with the rest of the subjects, work must be done so that schoolchildren acquire good healthy habits through an unconventional way, such as doing it through a gymkhana. Aim: Developing good habits in primary school students and learning in a playful and enjoyable way. Methods: Through a physical education session. Results & discussion: After completing the session, it is intended that the students have learned healthy habits through a gymkhana. Conclusions: Raise students’ awareness of good habits, since it has positive effects in personal, emotional and academic areas, and that you can learn in a different way, such as through gymkhana.Resumo: Introdução: Hoje, a taxa de excesso de peso aumentou, como também foi afetada pela diminuição dos esportes e pela falta de conhecimento sobre o que você está comendo. Assim, a partir da educação física, juntamente com o restante das disciplinas, é necessário trabalhar para que os alunos adquiram bons hábitos saudáveis de maneira não convencional, como por meio da gincana.Objectivos: Desenvolva bons hábitos nos alunos do ensino fundamental e aprenda de maneira divertida e divertida. Métodos: Através de uma sessão de educação física. Resultados e discussão: Após concluir a sessão, pretende-se que os alunos aprendam hábitos saudáveis através de uma gincana. Conclusões: Aumentar a conscientização dos alunos sobre os bons hábitos, uma vez que tem efeitos positivos nas áreas pessoal, emocional e acadêmica, e que pode ser aprendido de maneira diferente, como na gincana

On the deformation quantization of affine algebraic varieties

We compute an explicit algebraic deformation quantization for an affine Poisson variety described by an ideal in a polynomial ring, and inheriting its Poisson structure from the ambient space

Systemic sclerosis and pregnancy outcomes. A retrospective study from a single center

Background: Pregnancy in systemic sclerosis (SSc) patients is no more an infrequent event as it used to be, but literature data on pregnancy outcomes in women with SSc are scarce. The rate of preterm deliveries and intrauterine growth restriction (IUGR) seems to be increased, while the risk of miscarriages is controversial. Moreover, no study compared pregnancy outcomes in SSc with antiphospholipid syndrome (APS) and systemic lupus erythematosus (SLE). We performed a retrospective study to compare the pregnancy and disease outcomes of women with SSc with a cohort of age-matched women with systemic lupus erythematosus (SLE), antiphospholipid syndrome (APS), and healthy controls (HC). Methods: A total of 154 pregnancies from SSc, SLE, APS patients, and HC were prospectively followed at the High-Risk Pregnancy Unit of our center from 2008 to 2019. The primary outcome was a composite endpoint of miscarriages, fetal deaths, intrauterine growth restriction (IUGR), preeclampsia, neonatal deaths, preterm birth, and small-for-gestational-age (SGA) newborns. Single adverse pregnancy outcomes (APO) represented secondary endpoints. SSc activity variations in relation to pregnancy were assessed. Results: The risk of APO was significantly higher in SSc patients compared to HC (60.6% vs 10.0%; OR = 14.42; 95% CI 3.70-56.18, p = 0.001) and SLE patients (60.6% vs 37.5%; OR = 3.56; 95% CI 1.29-9.83, p = 0.014). Compared to HC, women with SSc had an increased frequency of first trimester miscarriage (15% vs 0 %; p = 0.016), preeclampsia (12% vs 0%, p = 0.038), and SGA newborns (21.2% vs 0%; p = 0.003). Preterm deliveries were more frequent in SSc pregnancies in comparison with HC (24.2% vs 5%; OR = 6.08; 95% CI 1.19-31.02, p = 0.036) and SLE patients (24.2% vs 7.5%, OR = 5.68; 95% CI 1.1-29.38, p = 0.038). Disease remained stable in all SSc patients during pregnancy and up to 1 year after delivery. Conclusions: We found an increased risk of APO in our SSc cohort in comparison with HC (with higher rates of miscarriages, preeclampsia, SGA newborns, and preterm deliveries) and SLE patients (presenting a higher rate of preterm deliveries). High-risk multidisciplinary management of SSc pregnant women is highly recommended

Kidney biopsy in lupus nephritis after achieving clinical renal remission: paving the way for renal outcome assessment.

The role of repeat kidney biopsy in lupus nephritis (LN) with renal remission is unclear. The aim of this study was to assess this role in a real-life scenario. This retrospective, single-centre study included 56 patients with LN diagnosed from 1998 to 2019, with an initial kidney biopsy (KB1) at the onset of LN and a second kidney biopsy (KB2) after achieving renal remission. A total of 51 (91.1%) patients were women with a median age of 29.9 years [interquartile range (IQR) 23.4-40.6] at the time of LN diagnosis. KB2s were performed after 41.1 months (IQR 30.1-52.5) of KB1. At the time of KB2, complete renal response was achieved in 51 (91.1%) patients. The median activity index decreased from a baseline value of 6.5 (IQR 2.8-11) to 0 (IQR 0-2) (P < .001). The chronicity index worsened from 1 (IQR 0-2) to 2 (IQR 1-3) (P = .01). In patients with proliferative/mixed forms at KB2, the chronicity index median value increased to 3 (IQR 1.5-4), as well as interstitial fibrosis and tubular atrophy [Formula: see text]25%, from 5.4% to 13.5%. Persistent histological active LN (activity index ≥2) was present in 11 (19.6%) KB2s. There were no differences when comparing immunological parameters between both groups (activity index ≥2 versus <2) at KB2, nor in the percentage of patients who presented renal flare. Immunosuppressive treatment was withdrawn in 35 (62.5%) patients and maintained/switched in 21 (37.5%). Afterward, new renal flare occurred in 9 patients per group (25.7% and 43%, respectively), after a median time of 39 months (IQR 6.5-55) and 7 months (IQR 6-30), respectively. There was no difference in the number of patients who developed chronic kidney disease [n = 14 (25%)] according to the treatment. In conclusion, KB2 provides valuable information to guide immunosuppressive maintenance therapy

Active site-directed inhibitors of prolyl oligopeptidase abolishes its conformational dynamics

Deciphering conformational dynamics is crucial for understanding the biological functions of proteins and for designing compounds targeting them. In particular, providing an accurate description of microsecond-millisecond motions opens the opportunity for regulating protein-protein interactions (PPIs) by modulating the dynamics of one interacting partner. Here we analyzed the conformational dynamics of prolyl oligopeptidase (POP) and the effects of active-site-directed inhibitors on the dynamics. We used an integrated structural biology approach based on NMR spectroscopy and SAXS experiments complemented by MD simulations. We found that POP is in a slow equilibrium in solution between open and closed conformations, and that inhibitors effectively abolished this equilibrium by stabilizing the enzyme in the closed conformation

Effective supergravity descriptions of superstring cosmology

This text is a review of aspects of supergravity theories that are relevant in superstring cosmology. In particular, it considers the possibilities and restrictions for `uplifting terms', i.e. methods to produce de Sitter vacua. We concentrate on N=1 and N=2 supergravities, and the tools of superconformal methods, which clarify the structure of these theories. Cosmic strings and embeddings of target manifolds of supergravity theories in others are discussed in short at the end.Comment: 12 pages, contribution to the proceedings of the 2nd international conference on Quantum Theories and Renormalization Group in Gravity and Cosmology, Barcelona, July 11-15, 2006, Journal of Physics