On L\'evy's Brownian motion indexed by the elements of compact groups

We investigate positive definiteness of the Brownian kernel K(x,y)=1/2(d(x,x_0) + d(y,x_0) - d(x,y)) on a compact group G and in particular for G=SO(n).Comment: Accepted for publication. 10 page

Representation of Gaussian Isotropic Spin Random Fields

We develop a technique for the construction of random fields on algebraic structures. We deal with two general situations: random fields on homogeneous spaces of a compact group and in the spin-line bundles of the 2-sphere. In particular, every spin Gaussian isotropic field can be obtained with this construction. Our construction extends P. L\'evy's original idea for the spherical Brownian Motion.Comment: 27 pages. Accepted for publication on Stoch. Processes App

Large Deviation asymptotics for the exit from a domain of the bridge of a general Diffusion

We provide Large Deviation estimates for the bridge of a $d$-dimensional general diffusion process as the conditioning time tends to $0$ and apply these results to the evaluation of the asymptotics of its exit time probabilities. We are motivated by applications to numerical simulation, especially in connection with stochastic volatility models.Comment: 15 pages, 2 figure

A Method for Manufacturing Oncological Phantoms for the Quantification of 18F-FDG PET and DW-MRI Studies

The aim of this work was to develop a method to manufacture oncological phantoms for quantitation purposes in 18F-FDG PET and DW-MRI studies. Radioactive and diffusion materials were prepared using a mixture of agarose and sucrose radioactive gels. T2 relaxation and diffusion properties of gels at different sucrose concentrations were evaluated. Realistic oncological lesions were created using 3D-printed plastic molds filled with the gel mixture. Once solidified, gels were extracted from molds and immersed in a low-radioactivity gel simulating normal background tissue. A breast cancer phantom was manufactured using the proposed method as an exploratory feasibility study, including several realistic oncological configurations in terms of both radioactivity and diffusion. The phantom was acquired in PET with 18F-FDG, immediately after solidification, and in DW-MRI the following day. Functional volumes characterizing the simulated BC lesions were segmented from PET and DW-MRI images. Measured radioactive uptake and ADC values were compared with gold standards. Phantom preparation was straightforward, and the time schedule was compatible with both PET and MRI measurements. Lesions appeared on 18F-FDG PET and DW-MRI images as expected, without visible artifacts. Lesion functional parameters revealed the phantom’s potential for validating quantification methods, in particular for new generation hybrid PET-MRI systems

To treat or not to treat: comparison of different criteria used to determine whether weight loss is to be recommended

Background: Excess body fat is a major risk factor for disease primarily due to its endocrine activity. In recent years several criteria have been introduced to evaluate this factor. Nevertheless, treatment need is currently assessed only on the basis of an individual's Body Mass Index (BMI), calculated as body weight (in kg) divided by height in m2. The aim of our study was to determine whether application of the BMI, compared to adiposity-based criteria, results in underestimation of the number of subjects needing lifestyle intervention. Methods: We compared treatment need based on BMI classification with four adiposity-based criteria: percentage body fat (%BF), considered both alone and in relation to metabolic syndrome risk (MS), waist circumference (WC), as an index of abdominal fat, and Body Fat Mass Index (BFMI, calculated as fat mass in kg divided by height in m2) in 63 volunteers (23 men and 40 women, aged 20 – 65 years). Results: According to the classification based on BMI, 6.3% of subjects were underweight, 52.4% were normal weight, 30.2% were overweight, and 11.1% were obese. Agreement between the BMI categories and the other classification criteria categories varied; the most notable discrepancy emerged in the underweight and overweight categories. BMI compared to almost all of the other adiposity-based criteria, identified a lower percentage of subjects for whom treatment would be recommended. In particular, the proportion of subjects for whom clinicians would strongly recommend weight loss on the basis of their BMI (11.1%) was significantly lower than those identified according to WC (25.4%, p = 0.004), %BF (28.6%, p = 0.003), and MS (33.9%, p = 0.002). Conclusion: The use of the BMI alone, as opposed to an assessment based on body composition, to identify individuals needing lifestyle intervention may lead to unfortunate misclassifications. Population-specific data on the relationships between body composition, morbidity, and mortality are needed to improve the diagnosis and treatment of at-risk individual

Representations of Gaussian isotropic spin random fields

Abstract We develop a technique for the construction of random fields on algebraic structures. We deal with two general situations: random fields on homogeneous spaces of a compact group and in the spin line bundles of the 2-sphere. In particular, every complex Gaussian isotropic spin random field can be represented in this way. Our construction extends P. Lévy's original idea for the spherical Brownian motion

On Sharp Large Deviations for the bridge of a general Diffusion

Abstract We provide sharp Large Deviation estimates for the probability of exit from a domain for the bridge of a d-dimensional general diffusion process X, as the conditioning time tends to 0. This kind of results is motivated by applications to numerical simulation. In particular we investigate the influence of the drift b of X. It turns out that the sharp asymptotics for the exit time probability are independent of the drift, provided b enjoyes a simple condition that is always satisfied in dimension 1. On the other hand, we show that the drift can be influential if this assumption is not satisfied

Autistic symptoms in Greig cephalopolysyndactyly syndrome: a family case report

Abstract Background Greig cephalopolysyndactyly syndrome is a rare multiple congenital anomaly syndrome characterized by the triad of polysyndactyly (preaxial or mixed preaxial and postaxial), macrocephaly, and ocular hypertelorism. Little is known about the neuropsychological phenotype and the developmental features of this syndrome. Case presentation We describe the clinical features of a 7-year-old Italian white boy affected by Greig cephalopolysyndactyly syndrome in comorbidity with autism spectrum disorder and the case of his 45-year-old white father, carrying the same point deletion (c.3677del) in the GLI3 gene and showing subclinical autistic symptoms. We performed a neuropsychiatric assessment of cognitive, adaptive, socio-communicative, and behavioral skills of the child. Concurrently, the father underwent his first psychiatric evaluation of cognitive skills and autistic symptoms. Conclusions We report the first clinical description of an association between autistic symptoms and Greig cephalopolysyndactyly syndrome in two members of the same family with the same genetic point deletion. Further research is required in order to draw an accurate conclusion regarding the association between Greig cephalopolysyndactyly syndrome and autism