The information content of option prices on the underlying asset has a special importance in finance. In particular, with the use of option implied trees, market participants may price other derivatives, estimate and forecast volatility (see e.g. the volatility index VIX), or higher moments of the underlying asset distribution. A crucial input of option implied trees is the estimation of the smile (implied volatility as a function of the strike price), which boils down to fitting a function to a limited number of existing knots. However, standard techniques require a one-to-one mapping between volatility and strike price, which is not met in the reality of financial markets, where, to a given strike price, two different implied volatilities are usually associated (coming from different types of options: call and put).\ud In this paper we compare the widely used methodology of discarding some implied volatilities and interpolating the remaining knots with cubic splines, to a fuzzy regression approach which does not require an a-priori choice of implied volatilities. To this end, we first extend some linear fuzzy regression methods to a polynomial form and we apply them to the financial problem. The fuzzy regression methods used range from the possibilistic regression method of Tanaka et al.[28], to theleast squares fuzzy regression method of Savic and Pedrycz [27]and to the hybrid method of Ishibuchi and Nii[11]

Background The incidence of the highly morbid and potentially lethal gangrenous cholecystitis was reportedly increased during the COVID-19 pandemic. The aim of the ChoCO-W study was to compare the clinical findings and outcomes of acute cholecystitis in patients who had COVID-19 disease with those who did not. Methods Data were prospectively collected over 6 months (October 1, 2020, to April 30, 2021) with 1-month follow-up. In October 2020, Delta variant of SARS CoV-2 was isolated for the first time. Demographic and clinical data were analyzed and reported according to the STROBE guidelines. Baseline characteristics and clinical outcomes of patients who had COVID-19 were compared with those who did not. Results A total of 2893 patients, from 42 countries, 218 centers, involved, with a median age of 61.3 (SD: 17.39) years were prospectively enrolled in this study; 1481 (51%) patients were males. One hundred and eighty (6.9%) patients were COVID-19 positive, while 2412 (93.1%) were negative. Concomitant preexisting diseases including cardiovascular diseases (p < 0.0001), diabetes (p < 0.0001), and severe chronic obstructive airway disease (p = 0.005) were significantly more frequent in the COVID-19 group. Markers of sepsis severity including ARDS (p < 0.0001), PIPAS score (p < 0.0001), WSES sepsis score (p < 0.0001), qSOFA (p < 0.0001), and Tokyo classification of severity of acute cholecystitis (p < 0.0001) were significantly higher in the COVID-19 group. The COVID-19 group had significantly higher postoperative complications (32.2% compared with 11.7%, p < 0.0001), longer mean hospital stay (13.21 compared with 6.51 days, p < 0.0001), and mortality rate (13.4% compared with 1.7%, p < 0.0001). The incidence of gangrenous cholecystitis was doubled in the COVID-19 group (40.7% compared with 22.3%). The mean wall thickness of the gallbladder was significantly higher in the COVID-19 group [6.32 (SD: 2.44) mm compared with 5.4 (SD: 3.45) mm; p < 0.0001]. Conclusions The incidence of gangrenous cholecystitis is higher in COVID patients compared with non-COVID patients admitted to the emergency department with acute cholecystitis. Gangrenous cholecystitis in COVID patients is associated with high-grade Clavien-Dindo postoperative complications, longer hospital stay and higher mortality rate. The open cholecystectomy rate is higher in COVID compared with non -COVID patients. It is recommended to delay the surgical treatment in COVID patients, when it is possible, to decrease morbidity and mortality rates. COVID-19 infection and gangrenous cholecystistis are not absolute contraindications to perform laparoscopic cholecystectomy, in a case by case evaluation, in expert hands. Graphical abstract

Frailty (FI) and metabolic syndrome (MS) are each associated with adverse health outcomes. A relationship between FI and MS has previously been described in adults. We considered the prevalence of a metabolically unhealthy phenotype (MUP) in malnourished children with neurological impairment and in subjects with obesity in comparison to a group of elderly individuals at risk of FI, and we did so in order to define the potential similarities that may underline the risk of FI in specific children. We considered 50 undernourished (defined as having a body mass index of BMI ≤ 2, standard deviation score, SDS, according to World Health Organization) disabled children; 50 children with obesity (BMI ≥ 2 SDS); 50 children who were a normal weight (−1 SDS ≤ BMI ≤ +1 SDS); 21 patients who were >75 years old. MUP was defined as the presence of at least one of the following risk factors: hypertension, hyperglycemia or diabetes, hypercholesterolemia, and hypertriglyceridemia. In children with a disability and obesity, a higher prevalence (p < 0.001) and risk (disability OR 54.88, obesity OR 13.37) of MUP was noted compared to children of a normal weight. Compared to elderly patients, the prevalence of MUP did not differ in disabled children. On the contrary, MUP was lower in children with obesity (p < 0.001) and in pediatric subjects of a normal weight (p < 0.01). MS might play a key role in “pediatric” frailty. The extremities of the aging process and malnutrition are likely key factors in the development of FI. A multidisciplinary approach to FI may represent an important milestone for pediatric care.

Totally implanted venous access ports (TIVAPs) have been established as effective and safe devices for oncologic patients. In breast cancer setting, the implant of the reservoir at mid-arm allows the absence of additional scars on the chest and the easier access to the port with significant cosmetic and psychological advantages. In the last decades, breast surgery has made great progresses to ameliorate the cosmetic results even in mastectomy techniques. In fact, many studies have demonstrated that negative body image perception affects physical and psychological wellbeing of survivors. Despite this evidence, limited importance is still reserved to TIVAPs placement site, which is traditionally the chest. It is not unusual to see patients after a nipple-sparing mastectomy with excellent cosmetic result who show a disfiguring scar on their upper chest due to TIVAP placement. We report the case of a young woman with BRCA2-related breast cancer who underwent bilateral nipple sparing mastectomy with immediate reconstruction and adjuvant chemotherapy. Her TIVAP was located at the mid-arm, which is still an uncommon site compared to the upper chest. An optimal cosmetic result was obtained both in breast reconstruction and in the arm site of port, with high-rate patient satisfaction. This case presentation aims to raise awareness towards women’s body image preservation, particularly in the choice of TIVAP placement: in most cases neckline and upper chest should be avoided for a better patient related outcome.

Neuroendocrine tumors represent the most common small bowel malignancy. At the time of presentation, they often debut as metastatic disease. Consensus guidelines recommend a multimodal and multidisciplinary approach that includes punctual investigations, aggressive surgical resection of the primary tumor and the assessment of possible synchronous metastasis through surgical procedures or ablative techniques. This report details the case of a 77-year-old male with a multifocal mid-gut neuroendocrine tumor with nodal dissemination and synchronous hepatic metastasis. He underwent a laparoscopic procedure that included an ileal resection with intracorporeal side-to-side ileo-ileal anastomosis, a large mesenteric nodal dissection extended up to superior mesenteric vein, a laparoscopic dissection of hepatic metastasis and an ultra-soundguided thermal ablation of two hepatic metastasis. This case highlights the efficacy of laparoscopy, providing a mini-invasive radical treatment and the importance of an aggressive multimodal approach in facing a metastatic multifocal mid-gut neuroendocrine tumor.