Abelian Functions for Trigonal Curves of Genus Three

We develop the theory of generalized Weierstrass sigma- and \wp-functions defined on a trigonal curve of genus three. In particular we give a list of the associated partial differential equations satisfied by the \wp-functions, a proof that the coefficients of the power series expansion of the sigma-function are polynomials of moduli parameters, and the derivation of two addition formulae.Comment: 32 pages, no figures. Revised version has the a fuller description of the general (3,4) trigonal curve results, the first version described only the "Purely Trigonal" cas

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

Characterization of two heparan sulphate-binding sites in the mycobacterial adhesin Hlp

<p>Abstract</p> <p>Background</p> <p>The histone-like Hlp protein is emerging as a key component in mycobacterial pathogenesis, being involved in the initial events of host colonization by interacting with laminin and glycosaminoglycans (GAGs). In the present study, nuclear magnetic resonance (NMR) was used to map the binding site(s) of Hlp to heparan sulfate and identify the nature of the amino acid residues directly involved in this interaction.</p> <p>Results</p> <p>The capacity of a panel of 30 mer synthetic peptides covering the full length of Hlp to bind to heparin/heparan sulfate was analyzed by solid phase assays, NMR, and affinity chromatography. An additional active region between the residues Gly46 and Ala60 was defined at the N-terminal domain of Hlp, expanding the previously defined heparin-binding site between Thr31 and Phe50. Additionally, the C-terminus, rich in Lys residues, was confirmed as another heparan sulfate binding region. The amino acids in Hlp identified as mediators in the interaction with heparan sulfate were Arg, Val, Ile, Lys, Phe, and Thr.</p> <p>Conclusion</p> <p>Our data indicate that Hlp interacts with heparan sulfate through two distinct regions of the protein. Both heparan sulfate-binding regions here defined are preserved in all mycobacterial Hlp homologues that have been sequenced, suggesting important but possibly divergent roles for this surface-exposed protein in both pathogenic and saprophic species.</p

Wave Solutions of Evolution Equations and Hamiltonian Flows on Nonlinear Subvarieties of Generalized Jacobians

The algebraic-geometric approach is extended to study solutions of N-component systems associated with the energy dependent Schrodinger operators having potentials with poles in the spectral parameter, in connection with Hamiltonian flows on nonlinear subvariaties of Jacobi varieties. The systems under study include the shallow water equation and Dym type equation. The classes of solutions are described in terms of theta-functions and their singular limits by using new parameterizations. A qualitative description of real valued solutions is provided

Closed geodesics and billiards on quadrics related to elliptic KdV solutions

We consider algebraic geometrical properties of the integrable billiard on a quadric Q with elastic impacts along another quadric confocal to Q. These properties are in sharp contrast with those of the ellipsoidal Birkhoff billiards. Namely, generic complex invariant manifolds are not Abelian varieties, and the billiard map is no more algebraic. A Poncelet-like theorem for such system is known. We give explicit sufficient conditions both for closed geodesics and periodic billiard orbits on Q and discuss their relation with the elliptic KdV solutions and elliptic Calogero systemComment: 23 pages, Latex, 1 figure Postscrip

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

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

Correspondence Between Cognitive and Audiological Evaluations Among the Elderly: A Preliminary Report of an Audiological Screening Model of Subjects at Risk of Cognitive Decline With Slight to Moderate Hearing Loss

Epidemiological studies show increasing prevalence rates of cognitive decline and hearing loss with age, particularly after the age of 65 years. These conditions are reported to be associated, although conclusive evidence of causality and implications is lacking. Nevertheless, audiological and cognitive assessment among elderly people is a key target for comprehensive and multidisciplinary evaluation of the subject's frailty status. To evaluate the use of tools for identifying older adults at risk of hearing loss and cognitive decline and to compare skills and abilities in terms of hearing and cognitive performances between older adults and young subjects, we performed a prospective cross-sectional study using supraliminal auditory tests. The relationship between cognitive assessment results and audiometric results was investigated, and reference ranges for different ages or stages of disease were determined. Patients older than 65 years with different degrees of hearing function were enrolled. Each subject underwent an extensive audiological assessment, including tonal and speech audiometry, Italian Matrix Sentence Test, and speech audiometry with logatomes in quiet. Cognitive function was screened and then verified by experienced clinicians using the Montreal Cognitive Assessment Score, the Geriatric Depression Scale, and further investigations in some. One hundred twenty-three subjects were finally enrolled during 2016-2019: 103 were >65 years of age and 20 were younger participants (as controls). Cognitive functions showed a correlation with the audiological results in post-lingual hearing-impaired patients, in particular in those affected by slight to moderate hearing loss and aged more than 70 years. Audiological testing can thus be useful in clinical assessment and identification of patients at risk of cognitive impairment. The study was limited by its sample size (CI 95%; CL 10%), strict dependence on language, and hearing threshold. Further investigations should be conducted to confirm the reported results and to verify similar screening models