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

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

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

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.

The Hamiltonian Structure of the Second Painleve Hierarchy

In this paper we study the Hamiltonian structure of the second Painleve hierarchy, an infinite sequence of nonlinear ordinary differential equations containing PII as its simplest equation. The n-th element of the hierarchy is a non linear ODE of order 2n in the independent variable $z$ depending on n parameters denoted by ${t}_1,...,{t}_{n-1}$ and $\alpha_n$. We introduce new canonical coordinates and obtain Hamiltonians for the $z$ and $t_1,...,t_{n-1}$ evolutions. We give explicit formulae for these Hamiltonians showing that they are polynomials in our canonical coordinates

Acute outcome after a single cryoballoon ablation: Comparison between Arctic Front Advance and Arctic Front Advance PRO

BACKGROUND: The novel fourth-generation cryoballoon (CB4) potentially allows for enhanced catheter maneuverability and more frequent capture of pulmonary vein (PV) potentials which can be used to monitor real-time PV isolation (PVI). The aim of our study is to compare the acute procedural endpoints between the CB4 and second-generation cryoballoon (CB2). METHODS: A single-center retrospective chart review was used to examine 50 consecutive patients with drug-refractory atrial fibrillation undergoing CB4-based PVI. Procedural data and acute success of these patients were compared to 50 propensity-matched controls who underwent cryoballoon ablation procedure using CB2. RESULTS: Procedures performed with the CB4 showed significant shorter fluoroscopy time (14.8 \ub1 5.5 vs 18.0 \ub1 6.5 minutes, P = .04), shorter procedure time (58.3 \ub1 15.7 vs 65.3 \ub1 21 minutes, P = .13), and shorter total ablation time (10.8 \ub1 1.5 vs 13.8 \ub1 1.9 minutes, P = .42). The real-time PVI visualization rate was 33.3% in the CB2 group and 74.7% in the CB4 group (P &lt; .001). CB4 was correlated to significant increase of acute real-time recordings with regard to all the single PV (left superior PV: 58% vs 84%, P = .02; left inferior PV: 26% vs 71%, P = .001; right superior PV 29% vs 61%, P = .01; and right inferior PV 19% vs 58%, P = .002). CONCLUSION: The CB4 was more often able to capture real-time recordings of PV potentials and the subsequent acute PV isolation

Design and in vitro study of a dual drug-loaded delivery system produced by electrospinning for the treatment of acute injuries of the central nervous system

Vascular and traumatic injuries of the central nervous system are recognized as global health priorities. A polypharmacology approach that is able to simultaneously target several injury factors by the combination of agents having synergistic effects appears to be promising. Herein, we designed a polymeric delivery system loaded with two drugs, ibuprofen (Ibu) and thyroid hormone triiodothyronine (T3) to in vitro release the suitable amount of the anti-inflammation and the remyelination drug. As a production method, electrospinning technology was used. First, Ibuloaded micro (diameter circa 0.95–1.20 µm) and nano (diameter circa 0.70 µm) fibers were produced using poly(L-lactide) PLLA and PLGA with different lactide/glycolide ratios (50:50, 75:25, and 85:15) to select the most suitable polymer and fiber diameter. Based on the in vitro release results and in-house knowledge, PLLA nanofibers (mean diameter = 580 ± 120 nm) loaded with both Ibu and T3 were then successfully produced by a co-axial electrospinning technique. The in vitro release studies demonstrated that the final Ibu/T3 PLLA system extended the release of both drugs for 14 days, providing the target sustained release. Finally, studies in cell cultures (RAW macrophages and neural stem cell-derived oligodendrocyte precursor cells—OPCs) demonstrated the anti-inflammatory and promyelinating efficacy of the dual drug-loaded delivery platform