Geometry of oblique projections

Let A be a unital C*-algebra. Denote by P the space of selfadjoint projections of A. We study the relationship between P and the spaces of projections P_a determined by the different involutions #_a induced by positive invertible elements a in A. The maps f_p: P \to P_a sending p to the unique q in P_a with the same range as p and \Omega_a: P_a \to P sending q to the unitary part of the polar decomposition of the symmetry 2q-1 are shown to be diffeomorphisms. We characterize the pairs of idempotents q, r in A with |q-r|<1 such that there exists a positive element a in A verifying that q, r are in P_a. In this case q and r can be joined by an unique short geodesic along the space of idempotents Q of A.Comment: 25 pages, Latex, to appear in Studia Mathematic

Projective spaces of a C*-algebra

Based on the projective matrix spaces studied by B. Schwarz and A. Zaks, we study the notion of projective space associated to a C*-algebra A with a fixed projection p. The resulting space P(p) admits a rich geometrical structure as a holomorphic manifold and a homogeneous reductive space of the invertible group of A. Moreover, several metrics (chordal, spherical, pseudo-chordal, non-Euclidean - in Schwarz-Zaks terminology) are considered, allowing a comparison among P(p), the Grassmann manifold of A and the space of positive elements which are unitary with respect to the bilinear form induced by the reflection e = 2p-1. Among several metrical results, we prove that geodesics are unique and of minimal length when measured with the spherical and non-Euclidean metrics.Comment: 26 pages, Late

Nullspaces and frames

In this paper we give new characterizations of Riesz and conditional Riesz frames in terms of the properties of the nullspace of their synthesis operators. On the other hand, we also study the oblique dual frames whose coefficients in the reconstruction formula minimize different weighted norms.Comment: 16 page

Evidence of Helicobacter sp. in dental plaque of captive dolphins (Tursiops gephyreus)

Gastrointestinal lesions have been extensively reported in wild and captive marine mammals. However, their etiology remains unclear. In humans and other animals, chronic gastritis and peptic ulcers have been associated with Helicobacter sp. Therefore, the aim of our study was to investigate the presence of Helicobacter sp. in the gastric juice, dental plaque, and saliva of marine mammals living in a controlled environment. Five dolphins (Tursiops gephyreus), one killer whale (Orcinus orca), one false killer whale (Pseudorca crassidens), three sea lions (Otaria flavescens), two elephant seals (Mirounga leonina), and two fur seals (Arctocephalus australis) were studied. Saliva, dental plaque, and gastric juice samples were examined for Helicobacter sp. using polymerase chain reaction. None of the gastric juice or saliva samples were positive for Helicobacter sp. However, Helicobacter sp. DNA was detected in dental plaque from two dolphins, suggesting the oral cavity might be a reservoir of this bacterium.Fil: Goldman, Cinthia Gabriela. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay; Argentina. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica; ArgentinaFil: Loureiro, Julio D.. Fundación Mundo Marino; ArgentinaFil: Quse, Viviana. Fundación Mundo Marino; ArgentinaFil: Corach, Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay; Argentina. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica; ArgentinaFil: Calderon, Enrique. Fundación Mundo Marino; ArgentinaFil: Caro, Ricardo A.. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica; ArgentinaFil: Boccio, José. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica; ArgentinaFil: Heredia, Sergio Rodríguez. Fundación Mundo Marino; ArgentinaFil: Di Carlo, Maria Beatriz. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica; ArgentinaFil: Zubillaga, Marcela Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay; Argentina. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica; Argentin

Mosaicism of alpha-synuclein gene rearrangements: Report of two unrelated cases of early-onset parkinsonism

Dear Sir, In genetics, the term ‘mosaicism’ describes the situation in which groups of cells have a different genetic composition to other cells in an organism. Somatic gene rearrangements due to multiplication or deletion of genes (copy number variation) and/or sections of chromosomes can lead to mosaicism. The presence of multiple copies of the alpha-synuclein gene (SNCA) is known to be associated with Parkinson’s disease (PD) and the severity of symptoms increases with the number of copies of the gene [1]. While the features of PD associated with duplication of SNCA are usually (but not always) typical of the condition [2–3], patients with triplicate copies have atypical features, including rapidly evolving symptoms, severe cognitive impairment, limited response to levodopa, more severe symptoms of dementia and more..

Hypothesis: Somatic Mosaicism and Parkinson Disease

Letter to the EditorFil: Perandones, Carlos Edgardo. Universidad de Buenos Aires. Facultad de Medicina. Hospital de Clínicas General San Martín; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay; ArgentinaFil: Pellene, L. A. Universidad de Buenos Aires. Facultad de Medicina. Hospital de Clínicas General San Martín; ArgentinaFil: Giugni, J. C.. Universidad de Buenos Aires. Facultad de Medicina. Hospital de Clínicas General San Martín; ArgentinaFil: Calvo, D. S.. Universidad de Buenos Aires. Facultad de Medicina. Hospital de Clínicas General San Martín; ArgentinaFil: Raina, G. B.. Universidad de Buenos Aires. Facultad de Medicina. Hospital de Clínicas General San Martín; ArgentinaFil: Cuevas, S. M.. Universidad de Buenos Aires. Facultad de Medicina. Hospital de Clínicas General San Martín; ArgentinaFil: Mata, I. F.. University of Washington; Estados UnidosFil: Zabetian, C. P.. University of Washington; Estados UnidosFil: Caputo, Mariela. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Servicio de Huellas Digitales Genéticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay; ArgentinaFil: Corach, Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay; Argentina. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Servicio de Huellas Digitales Genéticas; ArgentinaFil: Micheli, Federico. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Servicio de Huellas Digitales Genéticas; ArgentinaFil: Radrizzani Helguera, Martin. Universidad Nacional de San Martín. Escuela de Ciencia y Tecnología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay; Argentin

Transition Probability (Fidelity) and Its Relatives

Transition Probability (fidelity) for pairs of density operators can be defined as "functor" in the hierarchy of "all" quantum systems and also within any quantum system. The introduction of "amplitudes" for density operators allows for a more intuitive treatment of these quantities, also pointing to a natural parallel transport. The latter is governed by a remarkable gauge theory with strong relations to the Riemann-Bures metric.Comment: Talk at the 2009 Vaexoe Quantum Theory Conference. 11 page

Use of DNA technology in forensic dentistry

The established importance of Forensic Dentistry for human identification, mainly when there is little remaining material to perform such identification (e.g., in fires, explosions, decomposing bodies or skeletonized bodies), has led dentists working with forensic investigation to become more familiar with the new molecular biology techniques. The currently available DNA tests have high reliability and are accepted as legal proofs in courts. This article presents a literature review referring to the main studies on Forensic Dentistry that involve the use of DNA for human identification, and makes an overview of the evolution of this technology in the last years, highlighting the importance of molecular biology in forensic sciences

Letter to the Editor: Hypothesis: Somatic Mosaicism and Parkinson Disease

Fil: Perandones, Claudia. ANLIS Dr.C.G.Malbrán. Dirección Científico Técnica; Argentina.Fil: Pellene, Luis A. Universidad Nacional de Buenos Aires. Hospital de Clínicas. Programa de Parkinson y Movimientos Anormales; Argentina.Fil: Giugni, J. C. Universidad Nacional de Buenos Aires. Hospital de Clínicas. Programa de Parkinson y Movimientos Anormales; Argentina.Fil: Calvo, D. S. Universidad Nacional de Buenos Aires. Hospital de Clínicas. Programa de Parkinson y Movimientos Anormales; Argentina.Fil: Raina, G. B. Universidad Nacional de Buenos Aires. Hospital de Clínicas. Programa de Parkinson y Movimientos Anormales; Argentina.Fil: Cuevas, S. M. Universidad Nacional de Buenos Aires. Hospital de Clínicas. Programa de Parkinson y Movimientos Anormales; Argentina.Fil: Mata, Ignacio F. University of Washington and VA Puget Sound Health Care System, Seattle, Washington; Estados Unidos.Fil: Zabetian, Cyrus P. University of Washington and VA Puget Sound Health Care System, Seattle, Washington; Estados Unidos.Fil: Caputo, Mariela. Universidad de Buenos Aires. Escuela de Farmacia y Bioquímica. Servicio de Huellas Digitales Genéticas; Argentina.Fil: Corach, Daniel. Universidad de Buenos Aires. Escuela de Farmacia y Bioquímica. Servicio de Huellas Digitales Genéticas; Argentina.Fil: Micheli, Federico E. Universidad Nacional de Buenos Aires. Hospital de Clínicas. Programa de Parkinson y Movimientos Anormales; Argentina.Fil: Radrizzani, Martin. Universidad Nacional de San Martín. Escuela de Ciencia y Tecnología. Centro de Estudios en Salud y Medio Ambiente. Laboratorio de Citogenética Neuro y Molecular; Argentina