Geometric Poisson brackets on Grassmannians and conformal spheres

In this paper we relate the geometric Poisson brackets on the Grassmannian of 2-planes in R^4 and on the (2,2) Moebius sphere. We show that, when written in terms of local moving frames, the geometric Poisson bracket on the Moebius sphere does not restrict to the space of differential invariants of Schwarzian type. But when the concept of conformal natural frame is transported from the conformal sphere into the Grassmannian, and the Poisson bracket is written in terms of the Grassmannian natural frame, it restricts and results into either a decoupled system or a complexly coupled system of KdV equations, depending on the character of the invariants. We also show that the biHamiltonian Grassmannian geometric brackets are equivalent to the non-commutative KdV biHamiltonian structure. Both integrable systems and Hamiltonian structure can be brought back to the conformal sphere.Comment: 33 page

Pathological progression induced by the frontotemporal dementia-associated R406W tau mutation in patient-derived iPSCs

Mutations in the microtubule-associated protein tau (MAPT) gene are known to cause familial frontotemporal dementia (FTD). The R406W tau mutation is a unique missense mutation whose patients have been reported to exhibit Alzheimer\u27s disease (AD)-like phenotypes rather than the more typical FTD phenotypes. In this study, we established patient-derived induced pluripotent stem cell (iPSC) models to investigate the disease pathology induced by the R406W mutation. We generated iPSCs from patients and established isogenic lines using CRISPR/Cas9. The iPSCs were induced into cerebral organoids, which were dissociated into cortical neurons with high purity. In this neuronal culture, the mutant tau protein exhibited reduced phosphorylation levels and was increasingly fragmented by calpain. Furthermore, the mutant tau protein was mislocalized and the axons of the patient-derived neurons displayed morphological and functional abnormalities, which were rescued by microtubule stabilization. The findings of our study provide mechanistic insight into tau pathology and a potential for therapeutic intervention

The Cosmic Ray p+He energy spectrum in the 3-3000 TeV energy range measured by ARGO-YBJ

The ARGO-YBJ experiment is a full coverage air shower detector operated at the Yangbajing International Cosmic Ray Observatory. The detector has been in stable data taking in its full configuration since November 2007 to February 2013. The high altitude and the high segmentation and spacetime resolution offer the possibility to explore the cosmic ray energy spectrum in a very wide range, from a few TeV up to the PeV region. The high segmentation allows a detailed measurement of the lateral distribution, which can be used in order to discriminate showers produced by light and heavy elements. In this work we present the measurement of the cosmic ray light component spectrum in the energy range 3-3000 TeV. The analysis has been carried out by using a two-dimensional unfolding method based on the Bayes' theorem.Comment: Talk given at RICAP14 conferenc

Entanglement in fermionic systems

The anticommuting properties of fermionic operators, together with the presence of parity conservation, affect the concept of entanglement in a composite fermionic system. Hence different points of view can give rise to different reasonable definitions of separable and entangled states. Here we analyze these possibilities and the relationship between the different classes of separable states. We illustrate the differences by providing a complete characterization of all the sets defined for systems of two fermionic modes. The results are applied to Gibbs states of infinite chains of fermions whose interaction corresponds to a XY-Hamiltonian with transverse magnetic field.Comment: 13 pages, 3 figures, 4 table