Geometry of Lagrangian Grassmannians and nonlinear PDEs

This paper contains a thorough introduction to the basic geometric properties of the manifold of Lagrangian subspaces of a linear symplectic space, known as the Lagrangian Grassmannian. It also reviews the important relationship between hypersurfaces in the Lagrangian Grassmannian and second-order PDEs.Comment: 28 pages. Designed as opening contribution to the poceeding volume of the workshop "Geometry of Lagrangian Grassmannians and nonlinear PDEs" held in Warsaw, September 5-9, 2016. Changes in v3: small typos, updated bibliograph

The moment map on the space of symplectic 3D Monge-Amp\`ere equations

For any second-order scalar PDE $\mathcal{E}$ in one unknown function, that we interpret as a hypersurface of a second-order jet space $J^2$, we construct, by means of the characteristics of $\mathcal{E}$, a sub-bundle of the contact distribution of the underlying contact manifold $J^1$, consisting of conic varieties. We call it the contact cone structure associated with $\mathcal{E}$. We then focus on symplectic Monge-Amp\`ere equations in 3 independent variables, that are naturally parametrized by a 13-dimensional real projective space. If we pass to the field of complex numbers $\mathbb{C}$, this projective space turns out to be the projectivization of the 14-dimensional irreducible representation of the simple Lie group $\mathsf{Sp}(6,\mathbb{C})$: the associated moment map allows to define a rational map $\varpi$ from the space of symplectic 3D Monge-Amp\`ere equations to the projectivization of the space of quadratic forms on a $6$-dimensional symplectic vector space. We study in details the relationship between the zero locus of the image of $\varpi$, herewith called the cocharacteristic variety, and the contact cone structure of a 3D Monge-Amp\`ere equation $\mathcal{E}$: under the hypothesis of non-degenerate symbol, we prove that these two constructions coincide. A key tool in achieving such a result will be a complete list of mutually non-equivalent quadratic forms on a $6$-dimensional symplectic space, which has an interest on its own.Comment: v2, 41 pages, 1 figure, submitte

Apoptosis in human unfertilized oocytes after Intracytoplasmic Sperm Injection

Objective To investigate the presence of programmed cell death in unfertilized oocytes after intracytoplasmic sperm injection (ICSI), assuming that previous apoptotic events could be correlated with the fertilization failure. Design Comparison of the rate of DNA fragmentation in human oocytes at different stages of maturation soon after pick-up (control) and in unfertilized oocytes after ICSI treatment. Setting In vitro fertilization (IVF) laboratory with extensive ICSI experience. Patient(s) Sixty-three patients undergoing assisted fertilization by ICSI. Intervention(s) Terminal deoxynucleotidyl transferase-mediated digoxigenin-dUTP nick-end labeling (TUNEL) assay and anticaspase-3 cleaved immunoassay to detect apoptosis in control and ICSI-treated oocytes. Main Outcome Measure(s) Differences in the percentage of oocytes demonstrating DNA fragmentation between control oocytes and unfertilized ICSI treated oocytes at different stages of maturation. Result(s) The DNA fragmentation, by TUNEL assay, appeared in all the immature control oocytes, but only 37% of mature oocytes showed DNA fragmentation. This DNA fragmentation was observed in 88.8% of the oocytes unfertilized after ICSI; furthermore, DNA fragmentation appeared as well in the sperm injected into the cytoplasm. Conclusion(s) The study has shown DNA fragmentation in human oocytes unfertilized after ICSI. The evidence is confirmed as well in control oocytes, free from in vitro culture or manipulation stress. Caspase-3 immunoassay suggests the presence of apoptosis. The high percentage of oocytes demonstrating DNA fragmentation in the unfertilized oocytes could be correlated with fertilization failure

FSH administration reduces significantly sperm apoptosis only in the case of high DFI value: a study in idiopathic dispermic patients

Introduction: In the last decades sperm DNA quality has been recognized as one of the most important markers of male reproductive potential (Lewis and Aitken, 2005; Ozmen, 2007; Tarozzi, 2007), in contrast to standard semen parameters as sperm density, motility and morphology, which do not act as powerful discriminators between fertile and infertile men. DNA damage in the male germ line is a major contributor to infertility, miscarriage and birth defects in the offspring. In animal models, it has been unequivocally demonstrated that the genetic integrity of the male germ line plays a major role in determining the normality of embryonic development. In humans, many studies showed that sperm DNA damage is associated with impaired embryo cleavage (8), higher miscarriage rates (9) and also with a significantly increased risk of pregnancy loss after in vitro fertilization (IVF) and intracytoplasmic sperm injection (ICSI) (10). Specifically, above a threshold of 30% of sperms with fragmented DNA, chances for pregnancy are close to zero, either by means of natural conception or intrauterine insemination (Spano M, 2000; Bungum M, 2007). Since there is a clear relationship between sperm DNA damage and poor assisted reproduction technology (ART) outcomes, efforts should be directed in developing treatments to improve sperm DNA quality to be introduced into clinical use. The aim of this observational study was to investigate the effects of r-FSH administration on sperm DNA fragmentation of iOAT patients undergoing ICSI, comparing the DNA fragmentation index (DFI) before and after 90 days of FSH therapy. Matherial and Methods: Fifty-three iOAT men, with a median age of 33,6 ± 7,6 years, referred to our clinics because of fertility problems after at least two years of natural attempts, were selected for the study. In all patients DNA fragmentation was evaluated sperm prior to treatment with 150 IU of recombinant human FSH (GONAL-f®, Merck Serono) three times at week for at least three months. Patients were re-evaluated after a 3-month period with semen analysis and DNA fragmentation. Sperm DNA fragmentation index (DFI) was investigated by terminal deoxynucleotidyl transferase-mediated deoxyuridine triphosphate (dUTP) in situ DNA nick end labelling (TUNEL) assay. Data were analysed using the paired t-test and chi-square as appropriate. A p-value <0.05 was considered statistically significant. Results: After 3 months of r-FSH treatment, no significant differences was observed between baseline and post therapy semen sample parameters including sperm count, motility, and the percentage of normal sperm forms. IThe percentage of sperm DNA fragmentation in the total of patients dropped from 20.8 ± 9.1 to 15.1 ± 8.9 (P < 0.05) (see Tab I). Interestingly, no statistical difference was found in sperm DFI when patients showed a baseline DFI ≤15% (10.5 ± 4.2 vs 11.4 ± 4.5). We found an evident and statistically significant DFI reduction in patients with sperm baseline DFI value ≥15% (24.37 ± 9.6 vs 15.4 ± 4.6). Conclusion: Our data seems to demonstrate that FSH acts as a strong anti-apoptotic agent in reducing DNA fragmentation in iOAT patients. The therapy may be a specific pretreatment for infertile male partners of couples undergoing ICSI, specifically in the case that basal DFI is higher than 15%, reducing the percentage of spermatozoa with DNA integrity anomalies suggesting a positive effect on the reproductive outcome

Para- and perirenal ultrasonographic fat thickness is associated with 24-hours mean diastolic blood pressure levels in overweight and obese subjects

BACKGROUND: Renal sinus fat (RSF) has been recognized as a risk factor for arterial hypertension. This study was addressed to examine whether also para- and perirenal fat accumulation is associated to higher 24-h mean systolic (SBP) and/or diastolic blood pressure (DBP) levels in overweight and obese subjects. METHODS: A cohort of 42 overweight and obese patients, 29 women and 13 men, aged 25-55 years, not treated with any kind of drug, was examined. Body mass index (BMI), waist circumference (WC), fasting insulin and glucose serum levels, insulin resistance (assessed by using the homeostasis model assessment [HOMAIR]), and 24-h aldosterone urine levels were measured. Ambulatory blood pressure monitoring (ABPM) was measured with 15 min intervals from 7.0 a.m. to 11.0 a.m. and with 30 min intervals from 23.0 to 7.0 for consecutive 24 h, starting from 8:30 AM. Measurement of para- and perirenal fat thickness was performed by ultrasounds by a duplex Doppler apparatus. RESULTS: Para- and perirenal ultrasonographic fat thickness (PUFT) was significantly and positively correlated with WC (p &lt; 0.01), insulin (p &lt; 0.01), HOMAIR (p &lt; 0.01), and 24-h mean DBP levels (p &lt; 0.05). 24-h mean DBP was also significantly and positively correlated with 24-h aldosterone urine concentrations (p &lt; 0.001). A multivariate analysis by multiple linear regression was performed; the final model showed that the association of 24-h mean DBP as dependent variable with PUFT (multiple R = 0.34; p = 0.026) and daily aldosterone production (multiple R = 0.59; p = 0.001) was independent of other anthropometric, hormone and metabolic parameters. DISCUSSION AND CONCLUSIONS: This study shows a positive independent association between PUFT and mean 24-h diastolic blood pressure levels in overweight and obese subjects, suggesting a possible direct role of PUFT in increasing daily diastolic blood pressure

Colorectal cancer after bariatric surgery (Cric-Abs 2020): Sicob (Italian society of obesity surgery) endorsed national survey

Background The published colorectal cancer (CRC) outcomes after bariatric surgery (BS) are conflicting, with some anecdotal studies reporting increased risks. The present nationwide survey CRIC-ABS 2020 (Colo-Rectal Cancer Incidence-After Bariatric Surgery-2020), endorsed by the Italian Society of Obesity Surgery (SICOB), aims to report its incidence in Italy after BS, comparing the two commonest laparoscopic procedures-Sleeve Gastrectomy (SG) and Roux-en-Y gastric bypass (GBP). Methods Two online questionnaires-first having 11 questions on SG/GBP frequency with a follow-up of 5-10 years, and the second containing 15 questions on CRC incidence and management, were administered to 53 referral bariatric, high volume centers. A standardized incidence ratio (SIR-a ratio of the observed number of cases to the expected number) with 95% confidence intervals (CI) was calculated along with CRC incidence risk computation for baseline characteristics. Results Data for 20,571 patients from 34 (63%) centers between 2010 and 2015 were collected, of which 14,431 had SG (70%) and 6140 GBP (30%). 22 patients (0.10%, mean age = 53 +/- 12 years, 13 males), SG: 12 and GBP: 10, developed CRC after 4.3 +/- 2.3 years. Overall incidence was higher among males for both groups (SG: 0.15% vs 0.05%; GBP: 0.35% vs 0.09%) and the GBP cohort having slightly older patients. The right colon was most affected (n = 13) and SIR categorized/sex had fewer values &lt; 1, except for GBP males (SIR = 1.07). Conclusion Low CRC incidence after BS at 10 years (0.10%), and no difference between procedures was seen, suggesting that BS does not trigger the neoplasm development

Multicentre Italian study of SARS-CoV-2 infection in children and adolescents, preliminary data as at 10 April 2020

Data on features of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in children and adolescents are scarce. We report preliminary results of an Italian multicentre study comprising 168 laboratory-confirmed paediatric cases (median: 2.3 years, range: 1 day-17.7 years, 55.9% males), of which 67.9% were hospitalised and 19.6% had comorbidities. Fever was the most common symptom, gastrointestinal manifestations were frequent; two children required intensive care, five had seizures, 49 received experimental treatments and all recovered