Improved estimation of Fokker-Planck equations through optimisation

An improved method for the description of hierarchical complex systems by means of a Fokker-Planck equation is presented. In particular the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm for constraint problems (L-BFGS-B) is used to minimize the distance between the numerical solutions of the Fokker-Planck equation and the empirical probability density functions and thus to estimate properly the drift and diffusion term of the Fokker-Planck equation. The optimisation routine is applied to a time series of velocity measurements obtained from a turbulent helium gas jet in order to demonstrate the benefits and to quantify the improvements of this new optimisation routine

Dynamical model and nonextensive statistical mechanics of a market index on large time windows

The shape and tails of partial distribution functions (PDF) for a financial signal, i.e. the S&P500 and the turbulent nature of the markets are linked through a model encompassing Tsallis nonextensive statistics and leading to evolution equations of the Langevin and Fokker-Planck type. A model originally proposed to describe the intermittent behavior of turbulent flows describes the behavior of normalized log-returns for such a financial market index, for small and large time windows, both for small and large log-returns. These turbulent market volatility (of normalized log-returns) distributions can be sufficiently well fitted with a $\chi^2$-distribution. The transition between the small time scale model of nonextensive, intermittent process and the large scale Gaussian extensive homogeneous fluctuation picture is found to be at $ca.$ a 200 day time lag. The intermittency exponent ($\kappa$) in the framework of the Kolmogorov log-normal model is found to be related to the scaling exponent of the PDF moments, -thereby giving weight to the model. The large value of $\kappa$ points to a large number of cascades in the turbulent process. The first Kramers-Moyal coefficient in the Fokker-Planck equation is almost equal to zero, indicating ''no restoring force''. A comparison is made between normalized log-returns and mere price increments.Comment: 40 pages, 14 figures; accepted for publication in Phys Rev

IMPULSE: the impact of gender on the presentation and management of aortic stenosis across Europe.

AIMS: There is an increasing awareness of gender-related differences in patients with severe aortic stenosis and their outcomes after surgical aortic valve replacement (SAVR) and transcatheter aortic valve implantation (TAVI). METHODS: Data from the IMPULSE registry were analysed. Patients with severe aortic stenosis (AS) were enrolled between March 2015 and April 2017 and stratified by gender. A subgroup analysis was performed to assess the impact of age. RESULTS: Overall, 2171 patients were enrolled, and 48.0% were female. Women were characterised by a higher rate of renal impairment (31.7 vs 23.3%; p<0.001), were at higher surgical risk (EuroSCORE II: 4.5 vs 3.6%; p=0.001) and more often in a critical preoperative state (7.0vs 4.2%; p=0.003). Men had an increased rate of previous cardiac surgery (9.4 vs 4.7%; p<0.001) and a reduced left ventricular ejection fraction (4.9 vs 1.3%; p<0.001). Concomitant mitral and tricuspid valve disease was substantially more common among women. Symptoms were highly prevalent in both women and men (83.6 vs 77.3%; p<0.001). AVR was planned in 1379 cases. Women were more frequently scheduled to undergo TAVI (49.3 vs 41.0%; p<0.001) and less frequently for SAVR (20.3 vs 27.5%; p<0.001). CONCLUSIONS: The present data show that female patients with severe AS have a distinct patient profile and are managed in a different way to males. Gender-based differences in the management of patients with severe AS need to be taken into account more systematically to improve outcomes, especially for women

IMPULSE: The impact of gender on the presentation and management of aortic stenosis across Europe

Aims There is an increasing awareness of gender-related differences in patients with severe aortic stenosis and their outcomes after surgical aortic valve replacement (SAVR) and transcatheter aortic valve implantation (TAVI). Methods Data from the IMPULSE registry were analysed. Patients with severe aortic stenosis (AS) were enrolled between March 2015 and April 2017 and stratified by gender. A subgroup analysis was performed to assess the impact of age. Results Overall, 2171 patients were enrolled, and 48.0% were female. Women were characterised by a higher rate of renal impairment (31.7 vs 23.3%; p&lt;0.001), were at higher surgical risk (EuroSCORE II: 4.5 vs 3.6%; p=0.001) and more often in a critical preoperative state (7.0vs 4.2%; p=0.003). Men had an increased rate of previous cardiac surgery (9.4 vs 4.7%; p&lt;0.001) and a reduced left ventricular ejection fraction (4.9 vs 1.3%; p&lt;0.001). Concomitant mitral and tricuspid valve disease was substantially more common among women. Symptoms were highly prevalent in both women and men (83.6 vs 77.3%; p&lt;0.001). AVR was planned in 1379 cases. Women were more frequently scheduled to undergo TAVI (49.3 vs 41.0%; p&lt;0.001) and less frequently for SAVR (20.3 vs 27.5%; p&lt;0.001). Conclusions The present data show that female patients with severe AS have a distinct patient profile and are managed in a different way to males. Gender-based differences in the management of patients with severe AS need to be taken into account more systematically to improve outcomes, especially for women

Impact of selected comorbidities on the presentation and management of aortic stenosis

Background Contemporary data regarding the impact of comorbidities on the clinical presentation and management of patients with severe aortic stenosis (AS) are scarce. Methods Prospective registry of severe patients with AS across 23 centres in nine European countries. Results Of the 2171 patients, chronic kidney disease (CKD 27.3%), left ventricular ejection fraction (LVEF) &lt;50% (22.0%), atrial fibrillation (15.9%) and chronic obstructive pulmonary disease (11.4%) were the most prevalent comorbidities (49.3% none, 33.9% one and 16.8% ≥2 of these). The decision to perform aortic valve replacement (AVR) was taken in a comparable proportion (67%, 72% and 69%, in patients with 0, 1 and ≥2 comorbidities; p=0.186). However, the decision for TAVI was more common with more comorbidities (35.4%, 54.0% and 57.0% for no, 1 and ≥2; p&lt;0.001), while the decision for surgical AVR (SAVR) was decreased with increasing comorbidity burden (31.9%, 17.4% and 12.3%; p&lt;0.001). The proportion of patients with planned AVRs that were performed within 3 months was significantly higher in patients with 1 or ≥2 comorbidities than in those without (8.7%, 10.0% and 15.7%; p&lt;0.001). Furthermore, the mean time to AVR was significantly shorter in patients with one (30.5 days) or ≥2 comorbidities (30.8 days) than in those without (35.7 days; p=0.012). Patients with reduced LVEF tended to be offered an AVR more frequently and with a shorter delay while patients with CKD were less frequently treated. Conclusions Comorbidities in severe patients with AS affect the presentation and management of patients with severe AS. TAVI was offered more often than SAVR and performed within a shorter time period

Management of patients with severe aortic stenosis in the TAVI-era: How recent recommendations are translated into clinical practice

Objective Approximately 3.4% of adults aged &gt;75 years suffer from aortic stenosis (AS). Guideline indications for aortic valve replacement (AVR) distinguish between patients with symptomatic and asymptomatic severe AS. The present analysis aims to assess contemporary practice in the treatment of severe AS across Europe and identify characteristics associated with treatment decisions, namely denial of AVR in symptomatic patients and assignment of asymptomatic patients to AVR. Methods Participants of the prospective, multinational IMPULSE database of patients with severe AS were grouped according to AS symptoms, and stratified into subgroups based on assignment to/denial of AVR. Results Of 1608 symptomatic patients, 23.8% did not undergo AVR and underwent medical treatment. Denial was independently associated with multiple factors, including severe frailty (p=0.024); mitral (p=0.002) or tricuspid (p=0.004) regurgitation grade III/IV, and the presence of renal impairment (p=0.017). Of 392 asymptomatic patients, 86.5% had no prespecified indication for AVR. Regardless, 36.3% were assigned to valve replacement. Those with an indexed aortic valve area (AVA; p=0.045) or left ventricular ejection fraction (LVEF; p&lt;0.001) below the study median; or with a left ventricular end systolic diameter above the study median (p=0.007) were more likely to be assigned to AVR. Conclusions There may be considerable discrepancies between guideline-based recommendations and clinical practice decision-making in the treatment of AS. It appears that guidelines may not fully capture the complete clinical spectrum of patients with AS. Thus, there is a need to find ways to increase their acceptance and the rate of adoption

Symptoms, disease severity and treatment of adults with a new diagnosis of severe aortic stenosis

Objective Contemporary data on patients with previously undiagnosed severe aortic stenosis (AS) are scarce. We aimed to address this gap by gathering data from consecutive patients diagnosed with severe AS on echocardiography. Methods This was a prospective, multicentre, multinational, registry in 23 tertiary care hospitals across 9 European countries. Patients with a diagnosis of severe AS were included using echocardiography (aortic valve area (AVA) &lt;1 cm 2, indexed AVA &lt;0.6 cm 2 /m 2, maximum jet-velocity (V max) &gt;4 m/s and/or mean transvalvular gradient &gt;40 mm Hg). Results The 2171 participants had a mean age of 77.9 years and 48.0% were female. The mean AVA was 0.73 cm 2, V max 4.3 m/s and mean gradient 47.1 mm Hg; 62.1% had left ventricular hypertrophy and 27.3% an ejection fraction (EF) &lt;50%. 1743 patients (80.3%) were symptomatic (shortness-of-breath 91.0%; dizziness 30.2%, chest pain 28.9%). Patients had a EuroSCORE II of 4.0; 25.3% had a creatinine clearance &lt;50 mL/min, and 3.2% had an EF &lt;30%. Symptomatic patients were older and had more comorbidities than asymptomatic patients. Despite European Society of Cardiology 2017 valvular heart disease guideline class I recommendation, in only 76.2% a decision was made for an intervention (transcatheter 50.4%, surgical aortic valve replacement 25.8%). In asymptomatic patients, 57.7% with a class I/IIa indication were scheduled for a procedure, while 36.3% patients without an indication had their valve replaced. Conclusions The majority of patients with severe AS presented at an advanced disease stage. Management of severe AS remained suboptimal in a significant proportion of contemporary patients with severe AS. Trial registration number NCT02241447;Results