Integrability of graph combinatorics via random walks and heaps of dimers

We investigate the integrability of the discrete non-linear equation governing the dependence on geodesic distance of planar graphs with inner vertices of even valences. This equation follows from a bijection between graphs and blossom trees and is expressed in terms of generating functions for random walks. We construct explicitly an infinite set of conserved quantities for this equation, also involving suitable combinations of random walk generating functions. The proof of their conservation, i.e. their eventual independence on the geodesic distance, relies on the connection between random walks and heaps of dimers. The values of the conserved quantities are identified with generating functions for graphs with fixed numbers of external legs. Alternative equivalent choices for the set of conserved quantities are also discussed and some applications are presented.Comment: 38 pages, 15 figures, uses epsf, lanlmac and hyperbasic

Severe Aortic Stenosis and Myocardial Function: Diagnostic and Prognostic Usefulness of Ultrasonic Integrated Backscatter Analysis

Background— The aim of this study was to assess the myocardial reflectivity pattern in severe aortic valve stenosis through the use of integrated backscatter (IBS) analysis. Patients with aortic stenosis (AS) were carefully selected in the Department of Cardiology. Methods and Results— Thirty-five subjects (AS: valve orifice ≤1 cm2; 12 female; mean age, 71.8±6.2 years) and 25 healthy subjects were studied. All subjects of the study had conventional 2D-Doppler echocardiography and IBS. Backscatter signal was sampled at the septum and posterior wall levels. Patients with AS were divided into 2 groups: 16 patients with initial signs of congestive heart failure and a depressed left ventricular systolic function (DSF) (ejection fraction [EF] range, 35% to 50%) and 19 asymptomatic patients with normal left ventricular systolic function (NSF) (EF >50%). Myocardial echo intensity (pericardium related) was significantly higher at the septum and posterior wall levels in DSF than in NSF and in control subjects. IBS variation, as an expression of variation of the signal, appeared to be significantly lower in AS with DSF than in NSF and in control subjects, at both the septum and posterior wall levels. Patients with DSF underwent aortic valve replacement, and, during surgical intervention, a septal myocardial biopsy was made for evaluation of myocardium/fibrosis ratio. Abnormally increased echo intensity was detected in left ventricular pressure overload by severe aortic stenosis and correlated with increase of myocardial collagen content (operating biopsy). Conclusions— One year after aortic valve replacement, we observed a significant reduction of left ventricular mass, and, only if pericardial indexed IBS value (reduction of interstitial fibrosis) decreased, it was possible to observe an improvement of EF and of IBS variation

Cardiac resynchronization therapy after coronary sinus lead extraction: feasibility and mid-term outcome of transvenous reimplantation in a tertiary referral centre

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Transvenous removal of pacing and implantable cardiac defibrillating leads using single sheath mechanical dilatation and multiple venous approaches: high success rate and safety in more than 2000 leads

Abstract: The aim of the present study was to describe a 10 years single-centre experience in pacing and defibrillating leads removal using an effective and safe modified mechanical dilatation technique. We developed a single mechanical dilating sheath extraction technique with multiple venous entry site approaches. We performed a venous entry site approach (VEA) in cases of exposed leads and an alternative transvenous femoral approach (TFA) combined with an internal transjugular approach (ITA) in the presence of very tight binding sites causing failure of VEA extraction or in cases of free-floating leads. We attempted to remove 2062 leads [1825 pacing and 237 implantable cardiac defibrillating (ICD) leads; 1989 exposed at the venous entry site and 73 free-floating] in 1193 consecutive patients. The VEA was effective in 1799 leads, the TFA in 28, and the ITA in 205; in the overall population, we completely removed 2032 leads (98.4%), partially removed 18 (0.9%), and failed to remove 12 leads (0.6%). Major complications were observed in eight patients (0.7%), causing three deaths (0.3%). Mechanical single sheath extraction technique with multiple venous entry site approaches is effective, safe, and with a good cost effective profile for pacing and ICD leads removal

Aortic stiffness is associated with cardiac function and cerebral small vessel disease in patients with type 1 diabetes mellitus: assessment by magnetic resonance imaging

To evaluate, with the use of magnetic resonance imaging (MRI), whether aortic pulse wave velocity (PWV) is associated with cardiac left ventricular (LV) function and mass as well as with cerebral small vessel disease in patients with type 1 diabetes mellitus (DM). We included 86 consecutive type 1 DM patients (49 male, mean age 46.9 +/- 11.7 years) in a prospective, cross-sectional study. Exclusion criteria included aortic/heart disease and general MRI contra-indications. MRI of the aorta, heart and brain was performed for assessment of aortic PWV, as a marker of aortic stiffness, systolic LV function and mass, as well as for the presence of cerebral white matter hyperintensities (WMHs), microbleeds and lacunar infarcts. Multivariate linear or logistic regression was performed to analyse the association between aortic PWV and outcome parameters, with covariates defined as age, gender, mean arterial pressure, heart rate, BMI, smoking, DM duration and hypertension. Mean aortic PWV was 7.1 +/- 2.5 m/s. Aortic PWV was independently associated with LV ejection fraction ( = -0.406, P = 0.006), LV stroke volume ( = -0.407, P = 0.001), LV cardiac output ( = -0.458, P = 0.001), and with cerebral WMHs (P < 0.05). There were no independent associations between aortic stiffness and LV mass, cerebral microbleeds or lacunar infarcts. Aortic stiffness is independently associated with systolic LV function and cerebral WMHs in patients with type 1 DM.Neuro Imaging Researc