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

The quasi-bi-Hamiltonian formulation of the Lagrange top

Starting from the tri-Hamiltonian formulation of the Lagrange top in a six-dimensional phase space, we discuss the possible reductions of the Poisson tensors, the vector field and its Hamiltonian functions on a four-dimensional space. We show that the vector field of the Lagrange top possesses, on the reduced phase space, a quasi-bi-Hamiltonian formulation, which provides a set of separation variables for the corresponding Hamilton-Jacobi equation.Comment: 12 pages, no figures, LaTeX, to appear in J. Phys. A: Math. Gen. (March 2002

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.

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

Treatment of atrial fibrillation with a dual defibrillator in heart failure patients (TRADE HF): protocol for a randomized clinical trial.

Background: Heart failure(HF) and atrial fibrillation(AF) frequently coexist in the same patient and are associated with increased mortality and frequent hospitalizations. As the concomitance of AF and HF is often associated with a poor prognosis, the prompt treatment of AF in HF patients may significantly improve outcome.Methods/design: Recent implantable cardiac resynchronization (CRT) devices allow electrical therapies to treat AF automatically. TRADE-HF (trial registration: NCT00345592; http://www.clinicaltrials.gov) is a prospective, randomized, double arm study aimed at demonstrating the efficacy of an automatic, device-based therapy for treatment of atrial tachycardia and fibrillation(AT/AF) in patients indicated for CRT. The study compares automatic electrical therapy to a traditional more usual treatment of AT/AF: the goal is to demonstrate a reduction in a combined endpoint of unplanned hospitalizations for cardiac reasons, death from cardiovascular causes or permanent AF when using automatic atrial therapy as compared to the traditional approach involving hospitalization for symptoms and in-hospital treatment of AT/AF.Discussion: CRT pacemaker with the additional ability to convert AF as well as ventricular arrhythmias may play a simultaneous role in rhythm control and HF treatment. The value of the systematic implantation of CRT ICDs with the capacity to deliver atrial therapy in HF patients at risk of AF has not yet been explored. The TRADE-HF study will assess in CRT patients whether a strategy based on automatic management of atrial arrhythmias might be a valuable option to reduce the number of hospital admission and to reduce the progression the arrhythmia to a permanent for

Repeat Ablation for Atrial Fibrillation Recurrence Post Cryoballoon or Radiofrequency Ablation in the FIRE and ICE Trial

Background: The FIRE AND ICE trial assessed efficacy and safety of pulmonary vein (PV) isolation using cryoballoon versus radiofrequency current (RFC) ablation in patients with drug refractory, symptomatic, paroxysmal atrial fibrillation (AF). The purpose of the current study was to assess index lesion durability as well as reablation strategy and outcomes in trial patients undergoing a reablation procedure. Methods: Patients with reablation procedures during FIRE AND ICE were retrospectively consented and enrolled at 13 trial centers. The first reablation for each patient was included in the analysis. Documented arrhythmias before reablation, number and location of reconnected PVs, lesions created during reablations, procedural characteristics, and acute as well as long-term outcomes were assessed. Results: Eighty-nine (36 cryoballoon and 53 RFC) patients were included in this study. Paroxysmal atrial fibrillation was the predominant recurrent arrhythmia (69%) before reablation. Reablations occurred at a median of 173 and 182 days (P=0.54) in the cryoballoon and RFC cohorts, respectively. The number of reconnected PVs was significantly higher in the RFC than the cryoballoon group (2.1\ub11.4 versus 1.4\ub11.1; P=0.010), which was driven by significantly more reconnected left superior PVs and markedly more reconnected right superior PVs. The number of (predominantly RFC) lesions applied during reablation was significantly greater in patients originally treated with RFC (3.3\ub11.3 versus 2.5\ub11.5; P=0.015) with no difference in overall acute success (P=0.70). After reablation, no differences in procedure-related rehospitalization or antiarrhythmic drug utilization were observed between cohorts. Conclusions: At reablation, patients originally treated with the cryoballoon had significantly fewer reconnected PVs, which may reflect RFC catheter instability in certain left atrial regions, and thus required fewer lesions for reablation success. Repeat ablations were predominantly performed with RFC and resulted in similar acute success, duration of hospitalization, and antiarrhythmic drug prescription between the study cohorts. Clinical Trial Registration: URL: https://www.clinicaltrials.gov. Unique identifier: NCT03314753