Generalizations of entanglement based on coherent states and convex sets

Unentangled pure states on a bipartite system are exactly the coherent states with respect to the group of local transformations. What aspects of the study of entanglement are applicable to generalized coherent states? Conversely, what can be learned about entanglement from the well-studied theory of coherent states? With these questions in mind, we characterize unentangled pure states as extremal states when considered as linear functionals on the local Lie algebra. As a result, a relativized notion of purity emerges, showing that there is a close relationship between purity, coherence and (non-)entanglement. To a large extent, these concepts can be defined and studied in the even more general setting of convex cones of states. Based on the idea that entanglement is relative, we suggest considering these notions in the context of partially ordered families of Lie algebras or convex cones, such as those that arise naturally for multipartite systems. The study of entanglement includes notions of local operations and, for information-theoretic purposes, entanglement measures and ways of scaling systems to enable asymptotic developments. We propose ways in which these may be generalized to the Lie-algebraic setting, and to a lesser extent to the convex-cones setting. One of our original motivations for this program is to understand the role of entanglement-like concepts in condensed matter. We discuss how our work provides tools for analyzing the correlations involved in quantum phase transitions and other aspects of condensed-matter systems.Comment: 37 page

Characterization of vasa homolog in a neotropical catfish, Jundiá ( Rhamdia quelen ): Molecular cloning and expression analysis during embryonic and larval development

We have characterized the full-length vasa cDNA from Jundiá, Rhamdia quelen (Heptapteridae, Siluriformes). vasa encodes a member of the DEAD-box protein family of ATP-dependent RNA helicases. This protein is highly conserved among different organisms and its role is associated with RNA metabolism. In the majority of the investigated species, vasa is restricted to the germ cell lineage and its expression has been used to study germline development in many organisms, including fish. The deduced R. quelen vasa amino acid sequence displayed high similarity with Vasa protein sequences from other organisms, and did not cluster with PL10 or P68 DEAD-box protein subfamilies. We also reported that there is no other isoform for vasa mRNA in R. quelen gonads. Expression analysis by RT-PCR and qPCR showed vasa transcripts exclusively expressed in the germ cells of R. quelen gonads. R. quelen vasa mRNA was maternally inherited, and was detected in the migrating primordial germ cells (PGCs) until 264 h post-fertilization during embryonic and larval development. This work has characterized for the first time the full-length R. quelen vasa cDNA, and describes its expression patterns during R. quelen embryonic and larval development. Our results will contribute to the basic reproductive biology of this native species, and will support studies using vasa as a germ cell marker in different biotechnological studies, such as germ cell transplantation

Characterization of Gnrh/Gnih elements in the olfacto-retinal system and ovary during zebrafish ovarian maturation

Gonadotropin releasing hormone (GnRH) is one of the key players of brain-pituitary-gonad axis, exerting overall control over vertebrate reproduction. In zebrafish, two variants were characterized and named as Gnrh2 and Gnrh3. In this species, Gnrh3, the hypohysiotropic form, is expressed by neurons of the olfactory-retinal system, where it is related with food detection, intra/interspecific recognition, visual acuity and retinal processing modulation. Previous studies have reported the presence of Gnrh receptors in the zebrafish retina, but not yet in the zebrafish olfactory epithelium. The current study analyzed the presence of gnrh2 and gnrh3, their receptors (gnrhr 1,2,3 and 4) and gnih (gonadotropin inhibitory hormone) transcripts, as well as the Gnrh3 protein in the olfactory epithelium (OE), olfactory bulb (OB), retina and ovary during zebrafish ovarian maturation. We found an increase of gnrh receptors transcripts in the OE at the final stages of ovarian maturation. In the OE, Gnrh3 protein was detected in the olfactory receptor neurons cilia and in the olfactory nerve fibers. Interestingly, in the OB, we found an inverse expression pattern between gnih and gnrh3. In the retina, gnrhr4 mRNA was found in the nuclei of amacrine, bipolar, and ganglion cells next to Gnrh3 positive fibers. In the ovary, gnrh3, gnrhr2 and gnrhr4 transcripts were found in perinucleolar oocytes, while gnih in oocytes at the cortical alveolus stage. Our results suggested that Gnrh/Gnih elements are involved in the neuromodulation of the sensorial system particularly at the final stages of maturation, playing also a paracrine role in the ovary.Fil: Corchuelo, Sheryll. Universidade de Sao Paulo; BrasilFil: Martinez, Emanuel R. M.. Universidade de Sao Paulo; BrasilFil: Butzge, Arno J.. Universidade de Sao Paulo; BrasilFil: Doretto, Lucas B.. Universidade de Sao Paulo; BrasilFil: Ricci, Juliana M.B.. Universidade de Sao Paulo; BrasilFil: Valentin, Fernanda N.. Universidade de Sao Paulo; BrasilFil: Nakaghi, Laura S.O.. Universidade de Sao Paulo; BrasilFil: Somoza, Gustavo Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Biotecnológicas. Instituto de Investigaciones Biotecnológicas "Dr. Raúl Alfonsín" (sede Chascomús). Universidad Nacional de San Martín. Instituto de Investigaciones Biotecnológicas. Instituto de Investigaciones Biotecnológicas "Dr. Raúl Alfonsín" (sede Chascomús); ArgentinaFil: Nóbrega, Rafael H.. Universidade de Sao Paulo; Brasi