Quasi-BiHamiltonian Systems and Separability

Two quasi--biHamiltonian systems with three and four degrees of freedom are presented. These systems are shown to be separable in terms of Nijenhuis coordinates. Moreover the most general Pfaffian quasi-biHamiltonian system with an arbitrary number of degrees of freedom is constructed (in terms of Nijenhuis coordinates) and its separability is proved.Comment: 10 pages, AMS-LaTeX 1.1, to appear in J. Phys. A: Math. Gen. (May 1997

Generalized Lenard Chains, Separation of Variables and Superintegrability

We show that the notion of generalized Lenard chains naturally allows formulation of the theory of multi-separable and superintegrable systems in the context of bi-Hamiltonian geometry. We prove that the existence of generalized Lenard chains generated by a Hamiltonian function defined on a four-dimensional \omega N manifold guarantees the separation of variables. As an application, we construct such chains for the H\'enon-Heiles systems and for the classical Smorodinsky-Winternitz systems. New bi-Hamiltonian structures for the Kepler potential are found.Comment: 14 pages Revte

Reduction of bihamiltonian systems and separation of variables: an example from the Boussinesq hierarchy

We discuss the Boussinesq system with $t_5$ stationary, within a general framework for the analysis of stationary flows of n-Gel'fand-Dickey hierarchies. We show how a careful use of its bihamiltonian structure can be used to provide a set of separation coordinates for the corresponding Hamilton--Jacobi equations.Comment: 20 pages, LaTeX2e, report to NEEDS in Leeds (1998), to be published in Theor. Math. Phy

Early clinical predictors and correlates of long-term morbidity in bipolar disorder

OBJECTIVES: Identifying factors predictive of long-term morbidity should improve clinical planning limiting disability and mortality associated with bipolar disorder (BD). METHODS: We analyzed factors associated with total, depressive and mania-related long-term morbidity and their ratio D/M, as %-time ill between a first-lifetime major affective episode and last follow-up of 207 BD subjects. Bivariate comparisons were followed by multivariable linear regression modeling. RESULTS: Total % of months ill during follow-up was greater in 96 BD-II (40.2%) than 111 BD-I subjects (28.4%; P=0.001). Time in depression averaged 26.1% in BD-II and 14.3% in BD-I, whereas mania-related morbidity was similar in both, averaging 13.9%. Their ratio D/M was 3.7-fold greater in BD-II than BD-I (5.74 vs. 1.96; P<0.0001). Predictive factors independently associated with total %-time ill were: [a] BD-II diagnosis, [b] longer prodrome from antecedents to first affective episode, and [c] any psychiatric comorbidity. Associated with %-time depressed were: [a] BD-II diagnosis, [b] any antecedent psychiatric syndrome, [c] psychiatric comorbidity, and [d] agitated/psychotic depressive first affective episode. Associated with %-time in mania-like illness were: [a] fewer years ill and [b] (hypo)manic first affective episode. The long-term D/M morbidity ratio was associated with: [a] anxious temperament, [b] depressive first episode, and [c] BD-II diagnosis. CONCLUSIONS: Long-term depressive greatly exceeded mania-like morbidity in BD patients. BD-II subjects spent 42% more time ill overall, with a 3.7-times greater D/M morbidity ratio, than BD-I. More time depressed was predicted by agitated/psychotic initial depressive episodes, psychiatric comorbidity, and BD-II diagnosis. Longer prodrome and any antecedent psychiatric syndrome were respectively associated with total and depressive morbidity

On the integrability of stationary and restricted flows of the KdV hierarchy.

A bi--Hamiltonian formulation for stationary flows of the KdV hierarchy is derived in an extended phase space. A map between stationary flows and restricted flows is constructed: in a case it connects an integrable Henon--Heiles system and the Garnier system. Moreover a new integrability scheme for Hamiltonian systems is proposed, holding in the standard phase space.Comment: 25 pages, AMS-LATEX 2.09, no figures, to be published in J. Phys. A: Math. Gen.

A Left Atrial Appendage Closure Combined Procedure Review: past, present and future perspectives

Atrial fibrillation (AF) represents the most common cardiac arrhythmia worldwide; it poses a great burden in terms of quality of life reduction and yearly stroke risk. Left atrial appendage closure (LAAC) is a stroke prevention strategy that has been proven a viable alternative to anti-thrombotic regimens in non-valvular AF patients. LAAC can be performed as a stand-alone procedure or alongside a concomitant AF trans catheter ablation, in a procedure known as "Combined Procedure". Aim of this study is to summarize the scientific evidence backing this combined strategy

Structural-Functional Characterization and Physiological Significance of Ferredoxin-NADP+ Reductase from Xanthomonas axonopodis pv. citri

Xanthomonas axonopodis pv. citri is a phytopathogen bacterium that causes severe citrus canker disease. Similar to other phytopathogens, after infection by this bacterium, plants trigger a defense mechanism that produces reactive oxygen species. Ferredoxin-NADP+ reductases (FNRs) are redox flavoenzymes that participate in several metabolic functions, including the response to reactive oxygen species. Xanthomonas axonopodis pv. citri has a gene (fpr) that encodes for a FNR (Xac-FNR) that belongs to the subclass I bacterial FNRs. The aim of this work was to search for the physiological role of this enzyme and to characterize its structural and functional properties. The functionality of Xac-FNR was tested by cross-complementation of a FNR knockout Escherichia coli strain, which exhibit high susceptibility to agents that produce an abnormal accumulation of •O2-. Xac-FNR was able to substitute for the FNR in E. coli in its antioxidant role. The expression of fpr in X. axonopodis pv. citri was assessed using semiquantitative RT-PCR and Western blot analysis. A 2.2-fold induction was observed in the presence of the superoxide-generating agents methyl viologen and 2,3-dimethoxy-1,4-naphthoquinone. Structural and functional studies showed that Xac-FNR displayed different functional features from other subclass I bacterial FNRs. Our analyses suggest that these differences may be due to the unusual carboxy-terminal region. We propose a further classification of subclass I bacterial FNRs, which is useful to determine the nature of their ferredoxin redox partners. Using sequence analysis, we identified a ferredoxin (XAC1762) as a potential substrate of Xac-FNR. The purified ferredoxin protein displayed the typical broad UV-visible spectrum of [4Fe-4S] clusters and was able to function as substrate of Xac-FNR in the cytochrome c reductase activity. Our results suggest that Xac-FNR is involved in the oxidative stress response of Xanthomonas axonopodis pv. citri and performs its biological function most likely through the interaction with ferredoxin XAC1762

Differential Calculi on Associative Algebras and Integrable Systems

After an introduction to some aspects of bidifferential calculus on associative algebras, we focus on the notion of a "symmetry" of a generalized zero curvature equation and derive Backlund and (forward, backward and binary) Darboux transformations from it. We also recall a matrix version of the binary Darboux transformation and, inspired by the so-called Cauchy matrix approach, present an infinite system of equations solved by it. Finally, we sketch recent work on a deformation of the matrix binary Darboux transformation in bidifferential calculus, leading to a treatment of integrable equations with sources.Comment: 19 pages, to appear in "Algebraic Structures and Applications", S. Silvestrov et al (eds.), Springer Proceedings in Mathematics & Statistics, 202