Blow-up analysis for some mean field equations involving probability measures from statistical hydrodynamics

Motivated by the mean field equations with probability measure derived by Sawada-Suzuki and by Neri in the context of the statistical mechanics description of two-dimensional turbulence, we study the semilinear elliptic equation with probability measure: {equation*} -\Delta v=\lambda\int_I V(\alpha,x,v)e^{\alpha v}\,\Pda -\frac{\lambda}{|\Omega|}\iint_{I\times\Om}V(\alpha,x,v)e^{\alpha v}\,\Pda dx, {equation*} defined on a compact Riemannian surface. This equation includes the above mentioned equations of physical interest as special cases. For such an equation we study the blow-up properties of solution sequences. The optimal Trudinger-Moser inequality is also considered

On the blowup of solutions to Liouville type equations.

We estimate some complex structures related to perturbed Liouville equations defined on a compact Riemannian 2-manifold. As a byproduct, we obtain a quick proof of the mass quantization and we locate the blow-up points

Mass quantization and minimax solutions for Neri's mean field equation in 2D-turbulence

We study the mean field equation derived by Neri in the context of the statistical mechanics description of 2D-turbulence, under a ``stochastic" assumption on the vortex circulations. The corresponding mathematical problem is a nonlocal semilinear elliptic equation with exponential type nonlinearity, containing a probability measure $mathcal Pinmathcal M([-1,1])$ which describes the distribution of the vortex circulations. Unlike the more investigated ``deterministic" version, we prove that Neri's equation may be viewed as a perturbation of the widely analyzed standard mean field equation, obtained by taking $mathcal P=delta_1$. In particular, in the physically relevant case where $mathcal P$ is non-negatively supported and $mathcal P({1})>0$, we prove the mass quantization for blow-up sequences. We apply this result to construct minimax type solutions on bounded domains in $mathbb R^2$ and on compact 2-manifolds without boundary

Coronary Artery Bypass and Stroke: Incidence, Etiology, Pathogenesis, and Surgical Strategies to Prevent Neurological Complications

Current data suggest that cardiac bypass surgery is the single largest cause of iatrogenic stroke. Among the strategies to decrease or eliminate aortic manipulation, there is the use of off-pump coronary artery bypass grafting (CABG) through an aortic “no touch” technique, which reduces significantly the stroke rate. However, this off-pump aortic “no touch” technique is not always applicable, and, when saphenous vein and/or free arterial aortocoronary grafts are used, there is still risk of neurological injury due to tangential aortic clamp applied during the proximal anastomosis sewing. We aim to analyze the current incidence, etiology, and physiopathology of the neurological complications after coronary artery bypass surgery. We describe the methods and techniques that provide reduction in the occurrence of neurological complications. CABG with multiple clamp technique failed to find a better outcome in terms of neuropsychological deficit in the OPCABG group. By the way, patients undergoing CABG with single clamping seems to have better outcomes, suggesting that the cross-clamping technique used and minimal aortic manipulation could have had a role in reducing neurocognitive impairment. Moreover, surprisingly, CPB seemed to be a neuroprotective factor, and this aspect could be linked to the mild hypothermia used during on-pump surgery

Current and future options for adult biventricular assistance: a review of literature

In cardiogenic shock various short-term mechanical assistances may be employed, including an Extra Corporeal Membrane Oxygenator and other non-dischargeable devices. Once hemodynamic stabilization is achieved and the patient evolves towards a persisting biventricular dysfunction or an underlying long-standing end-stage disease is present, aside from Orthotopic Heart Transplantation, a limited number of long-term therapeutic options may be offered. So far, only the Syncardia Total Artificial Heart and the Berlin Heart EXCOR (which is not approved for adult use in the United States unlike in Europe) are available for extensive implantation. In addition to this, the strategy providing two continuous-flow Left Ventricular Assist Devices is still off-label despite its widespread use. Nevertheless, every solution ensures at best a 70% survival rate (reflecting both the severity of the condition and the limits of mechanical support) with patients suffering from heavy complications and a poor quality of life. The aim of the present paper is to summarize the features, implantation techniques, and results of current devices used for adult Biventricular Mechanical Circulatory Support, as well as a glance to future options

Cardiac surgery in the time of the novel coronavirus:Why we should think to a new normal

On 11 March 2020, the World Health Organization declared the SARS-CoV-2 outbreak a pandemic. At the time of writing, 24 May 2020 more than 5 million individuals have been tested positive and the death toll was over 330 000 deaths worldwide. The initial data pointed out the tight bond between cardiovascular diseases and worse health outcomes in COVID19-patients. Epidemiologically speaking, there is an overlap between the age-groups more affected by COVID-related death and the age-groups in which Cardiac Surgery has its usual base of patients. The Cardiac Surgery Departments have to think to anew normal: since the virus will remain endemic in the society, dedicated pathways or even dedicated Teams are pivotal to treat safely the patients, in respect of the safety of the health care workers. Moreover, we need a keen eye on deciding which pathologies have to be treated with priority: Coronary artery Disease showed a higher mortality rate in patients affected by COVID19, but it is, however, reasonable to think that all the cardiac pathologies affecting the lung circulation-such as symptomatic severe mitral diseases or aortic stenosis-might deserve a priority access to treatment, to increase the survival rate in case of an acquired-Coronavirus infection later on

Polychlorinated Biphenyls (PCBs) in the Environment: Occupational and Exposure Events, Effects on Human Health and Fertility

In the last decade or so, polychlorinated biphenyls (PCBs) garnered renewed attention in the scientific community due to new evidence pointing at their continued presence in the environment and workplaces and the potential human risks related to their presence. PCBs move from the environment to humans through different routes; the dominant pathway is the ingestion of contaminated foods (fish, seafood and dairy products), followed by inhalation (both indoor and outdoor air), and, to a lesser extent, dust ingestion and dermal contact. Numerous studies reported the environmental and occupational exposure to these pollutants, deriving from building materials (flame-retardants, plasticizers, paints, caulking compounds, sealants, fluorescent light ballasts, etc.) and electrical equipment. The highest PCBs contaminations were detected in e-waste recycling sites, suggesting the need for the implementation of remediation strategies of such polluted areas to safeguard the health of workers and local populations. Furthermore, a significant correlation between PCB exposure and increased blood PCB concentrations was observed in people working in PCB-contaminated workplaces. Several epidemiological studies suggest that environmental and occupational exposure to high concentrations of PCBs is associated with different health outcomes, such as neuropsychological and neurobehavioral deficits, dementia, immune system dysfunctions, cardiovascular diseases and cancer. In addition, recent studies indicate that PCBs bioaccumulation can reduce fertility, with harmful effects on the reproductive system that can be passed to offspring. In the near future, further studies are needed to assess the real effects of PCBs exposure at low concentrations for prolonged exposure in workplaces and specific indoor environments

Immigrants in agricultural sector in Sicily: the experience of Sicilia Integra project

The overview of the most relevant literature on migration, whose main issues were human rights, work in agriculture, cultural and social inclusion, highlighted one common point: the need to foster the legal work of migrants as a driver for social integration. This finding was confirmed by a CREA-PB survey that, after outlining the role of foreign workers in Sicilian agriculture, has emphasised how their state of isolation derived mainly from their bad housing conditions directly connected to illegal employment. The evaluation of the project “Sicilia Integra”, which was born under the patronage of the UN to include young immigrants in urban agriculture activities in Sicily, was carried out through the SWOT methodology for verifying if it could be spread in the Sicilian region