Isospectral Flow and Liouville-Arnold Integration in Loop Algebras

A number of examples of Hamiltonian systems that are integrable by classical means are cast within the framework of isospectral flows in loop algebras. These include: the Neumann oscillator, the cubically nonlinear Schr\"odinger systems and the sine-Gordon equation. Each system has an associated invariant spectral curve and may be integrated via the Liouville-Arnold technique. The linearizing map is the Abel map to the associated Jacobi variety, which is deduced through separation of variables in hyperellipsoidal coordinates. More generally, a family of moment maps is derived, identifying certain finite dimensional symplectic manifolds with rational coadjoint orbits of loop algebras. Integrable Hamiltonians are obtained by restriction of elements of the ring of spectral invariants to the image of these moment maps. The isospectral property follows from the Adler-Kostant-Symes theorem, and gives rise to invariant spectral curves. {\it Spectral Darboux coordinates} are introduced on rational coadjoint orbits, generalizing the hyperellipsoidal coordinates to higher rank cases. Applying the Liouville-Arnold integration technique, the Liouville generating function is expressed in completely separated form as an abelian integral, implying the Abel map linearization in the general case.Comment: 42 pages, 2 Figures, 1 Table. Lectures presented at the VIIIth Scheveningen Conference, held at Wassenaar, the Netherlands, Aug. 16-21, 199

Some remarks on the hyperelliptic moduli of genus 3

In 1967, Shioda \cite{Shi1} determined the ring of invariants of binary octavics and their syzygies using the symbolic method. We discover that the syzygies determined in \cite{Shi1} are incorrect. In this paper, we compute the correct equations among the invariants of the binary octavics and give necessary and sufficient conditions for two genus 3 hyperelliptic curves to be isomorphic over an algebraically closed field $k$, $\ch k \neq 2, 3, 5, 7$. For the first time, an explicit equation of the hyperelliptic moduli for genus 3 is computed in terms of absolute invariants.Comment: arXiv admin note: text overlap with arXiv:1209.044

Herpes zoster vaccination in the elderly subjects: improving awareness and uptake

Armando Stefanati, Nicoletta Valente, Silvia Lupi, Sara Previato, Matilde Giordani, Giovanni Gabutti Department of Medical Sciences, University of Ferrara, Ferrara, Italy Abstract: Herpes zoster (HZ) is a common disease in adults and older subjects solely related to the reactivation of latent varicella zoster virus in ganglia. The incidence of the disease increases with aging and the decline of varicella zoster virus-specific cell-mediated immunity. HZ has a significant impact on the quality of life of subjects during the acute phase. Besides, pain can persist even for a long time becoming chronic. The chronic pain following HZ is called postherpetic neuralgia, and it is a debilitating long-lasting condition, characterized by metameric pain, allodynia, and hyperalgesia. Therapeutic options against HZ and postherpetic neuralgia are often suboptimal and the impact of the disease and its complications on daily living activities is significant, especially in older subjects. Nowadays, a preventive approach to the disease is possible; as a matter of fact, a high-antigen content live vaccine is available. This vaccine has a good profile in terms of immunogenicity, efficacy, effectiveness, and safety and its use may prevent both HZ and postherpetic neuralgia. Nevertheless, the evaluation of the issues raised in countries that introduced this immunization show that both provider and patient barriers could have prevented a more robust uptake of HZ vaccination. In the USA, HZ immunization storage was expensive, reimbursement was cumbersome, and supply shortages may have limited promotion by the interests of the manufacturer and provider. The doctors did not actively recommend HZ vaccination; on the other hand, subjects were mostly unaware of the HZ vaccine. Several demographic factors, including sex and educational level, could have negatively affected the coverage rates; besides, the clinicians who treat adults focus less on vaccination than those taking care of children. On the other hand, when health care professionals undertook every effort to maximize the uptake of the shingles vaccine (eg, in the UK), the vaccine coverage rate increased very quickly. Keywords: herpes zoster, postherpetic neuralgia, vaccin

Peakons, R-Matrix and Toda-Lattice

The integrability of a family of hamiltonian systems, describing in a particular case the motionof N ``peakons" (special solutions of the so-called Camassa-Holm equation) is established in the framework of the $r$-matrix approach, starting from its Lax representation. In the general case, the $r$-matrix is a dynamical one and has an interesting though complicated structure. However, for a particular choice of the relevant parameters in the hamiltonian (the one corresponding to the pure ``peakons" case), the $r$-matrix becomes essentially constant, and reduces to the one pertaining to the finite (non-periodic) Toda lattice. Intriguing consequences of such property are discussed and an integrable time discretisation is derived.Comment: 12 plain tex page

Akns Hierarchy, Self-Similarity, String Equations and the Grassmannian

In this paper the Galilean, scaling and translational self--similarity conditions for the AKNS hierarchy are analysed geometrically in terms of the infinite dimensional Grassmannian. The string equations found recently by non--scaling limit analysis of the one--matrix model are shown to correspond to the Galilean self--similarity condition for this hierarchy. We describe, in terms of the initial data for the zero--curvature 1--form of the AKNS hierarchy, the moduli space of these self--similar solutions in the Sato Grassmannian. As a byproduct we characterize the points in the Segal--Wilson Grassmannian corresponding to the Sachs rational solutions of the AKNS equation and to the Nakamura--Hirota rational solutions of the NLS equation. An explicit 1--parameter family of Galilean self--similar solutions of the AKNS equation and the associated solution to the NLS equation is determined.Comment: 25 pages in AMS-LaTe

Avaliação de diferentes métodos de colheita de embriões bovinos.

Edição dos resumos da 20. Reunião Anual da Sociedade Brasileira de Tecnologia de Embriões, Araxá, MG, agosto 2006

Trypanosoma cruzi Adjuvants Potentiate T Cell-Mediated Immunity Induced by a NY-ESO-1 Based Antitumor Vaccine

Immunological adjuvants that induce T cell-mediate immunity (TCMI) with the least side effects are needed for the development of human vaccines. Glycoinositolphospholipids (GIPL) and CpGs oligodeoxynucleotides (CpG ODNs) derived from the protozoa parasite Trypanosoma cruzi induce potent pro-inflammatory reaction through activation of Toll-Like Receptor (TLR)4 and TLR9, respectively. Here, using mouse models, we tested the T. cruzi derived TLR agonists as immunological adjuvants in an antitumor vaccine. For comparison, we used well-established TLR agonists, such as the bacterial derived monophosphoryl lipid A (MPL), lipopeptide (Pam3Cys), and CpG ODN. All tested TLR agonists were comparable to induce antibody responses, whereas significant differences were noticed in their ability to elicit CD4+ T and CD8+ T cell responses. In particular, both GIPLs (GTH, and GY) and CpG ODNs (B344, B297 and B128) derived from T. cruzi elicited interferon-gamma (IFN-γ) production by CD4+ T cells. On the other hand, the parasite derived CpG ODNs, but not GIPLs, elicited a potent IFN-γ response by CD8+ T lymphocytes. The side effects were also evaluated by local pain (hypernociception). The intensity of hypernociception induced by vaccination was alleviated by administration of an analgesic drug without affecting protective immunity. Finally, the level of protective immunity against the NY-ESO-1 expressing melanoma was associated with the magnitude of both CD4+ T and CD8+ T cell responses elicited by a specific immunological adjuvant

Extranuclear structural components that mediate dynamic chromosome movements in yeast meiosis

Telomere-led rapid chromosome movements or rapid prophase movements direct fundamental meiotic processes required for successful haploidization of the genome. Critical components of the machinery that generates rapid prophase movements are unknown, and the mechanism underlying rapid prophase movements remains poorly understood. We identified S. cerevisiae Mps2 as the outer nuclear membrane protein that connects the LINC complex with the cytoskeleton. We also demonstrate that the motor Myo2 works together with Mps2 to couple the telomeres to the actin cytoskeleton. Further, we show that Csm4 interacts with Mps2 and is required for perinuclear localization of Myo2, implicating Csm4 as a regulator of the Mps2-Myo2 interaction. We propose a model in which the newly identified functions of Mps2 and Myo2 cooperate with Csm4 to drive chromosome movements in meiotic prophase by coupling telomeres to the actin cytoskeleton.Fil: Lee, Chih Ying. Oklahoma Medical Research Foundation; Estados UnidosFil: Bisig, Carlos Gaston. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigaciones en Química Biológica de Córdoba. Universidad Nacional de Córdoba. Facultad de Ciencias Químicas. Centro de Investigaciones en Química Biológica de Córdoba; ArgentinaFil: Conrad, Michael M.. Oklahoma Medical Research Foundation; Estados UnidosFil: Ditamo, Yanina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigaciones en Química Biológica de Córdoba. Universidad Nacional de Córdoba. Facultad de Ciencias Químicas. Centro de Investigaciones en Química Biológica de Córdoba; ArgentinaFil: Previato de Almeida, Luciana. Oklahoma Medical Research Foundation; Estados UnidosFil: Dresser, Michael E.. Oklahoma Medical Research Foundation; Estados UnidosFil: Pezza, Roberto J.. Oklahoma Medical Research Foundation; Estados Unido

On Separation of Variables for Integrable Equations of Soliton Type

We propose a general scheme for separation of variables in the integrable Hamiltonian systems on orbits of the loop algebra $\mathfrak{sl}(2,\Complex)\times \mathcal{P}(\lambda,\lambda^{-1})$. In particular, we illustrate the scheme by application to modified Korteweg--de Vries (MKdV), sin(sinh)-Gordon, nonlinear Schr\"odinger, and Heisenberg magnetic equations.Comment: 22 page