Constrained Mean Field Games Equilibria as Fixed Point of Random Lifting of Set-Valued Maps

We introduce an abstract framework for the study of general mean field game and mean field control problems. Given a multiagent system, its macroscopic description is provided by a time-depending probability measure, where at every instant of time the measure of a set represents the fraction of (microscopic) agents contained in it. The trajectories available to each of the microscopic agents are affected also by the overall state of the system. By using a suitable concept of random lift of set-valued maps, together with fixed point arguments, we are able to derive properties of the macroscopic description of the system from properties of the set-valued map expressing the admissible trajectories for the microscopical agents. We apply the results in the case in which the admissible trajectories of the agents are the minimizers of a suitable integral functional depending also from the macroscopic evolution of the system. Copyright (C) 2022 The Authors

Focus on diffusion MR investigations of musculoskeletal tissue to improve osteoporosis diagnosis: A brief practical review

Nowadays, a huge number of papers have documented the ability of diffusion magnetic resonance imaging (D-MRI) to highlight normal and pathological conditions in a variety of cerebral, abdominal, and cardiovascular applications. To date, however, the role of D-MRI to investigate musculoskeletal tissue, specifically the cancellous bone, has not been extensively explored. In order to determine potentially useful applications of diffusion techniques in musculoskeletal investigation, D-MRI applications to detect osteoporosis disease were reviewed and further explained

Diffusion tensor imaging and magnetic resonance spectroscopy assessment of cancellous bone quality in femoral neck of healthy, osteopenic and osteoporotic subjects at 3T: Preliminary experience.

We assessed the potential of diffusion tensor imaging (DTI) in combination with proton magnetic resonance spectroscopy ((1)H-MRS), in cancellous bone quality evaluation of the femoral neck in postmenopausal women. INTRODUCTION: DTI allows for non-invasive microarchitectural characterization of heterogeneous tissue. In this work we hypothesized that DTI parameters mean diffusivity (MD) and fractional anisotropy (FA) of bone marrow water, can provide information about microstructural changes that occur with the development of osteoporosis disease. Because osteoporosis is associated with increased bone marrow fat content, which in principal can alter DTI parameters, the goal of this study was to examine the potential of MD and FA, in combination with bone marrow fat fraction (FF), to discriminate between healthy, osteopenic and osteoporotic subjects, classified according to DXA criteria. MATERIALS AND METHODS: Forty postmenopausal women (mean age, 68.7years; range 52-81years), underwent a Dual-energy X-ray absorptiometry (DXA) examination in femoral neck, to be classified as healthy (n=12), osteopenic (n=14) and osteoporotic (n=14) subjects. (1)H-MRS and DTI (with b value=2500s/mm(2)) of femoral neck were obtained in each subject at 3T. The study protocol was approved by local Ethics Committee. MD, FA, FF and MD/FF, FA/FF were obtained and compared among the three bone-density groups. One-way ANOVA with multiple comparisons Bonferroni test and Pearson correlation analysis were applied. Receiver operating characteristic (ROC) curve analysis was also performed. RESULTS: Reproducibility of DTI measures was satisfactory. CV was approximately 2%-3% for MD and 4%-5% for FA measurements. Moreover, no significant difference was found in both MD and FA measurements between two separate sessions (median 34days apart) comprised of six healthy volunteers. FF was able to discriminate between healthy and osteoporotic subjects only. Conversely MD and FA were able to discriminate healthy from osteopenic and healthy from osteoporotic subjects, but they were not able to discriminate between osteopenic and osteoporotic patients. A significant correlation between MD and FF was observed in healthy group only. A moderate correlation was found between MD and T-score when all groups together are considered. No significant correlation was found between MD and T-score within groups. A significant positive correlation between FA and FF was found in both osteopenic and osteoporotic groups. Vice-versa no correlation between FA and FF was observed in healthy group. A high significant positive correlation was found between FA and T-score in all groups together, in healthy and in osteoporotic groups. MD/FF and FA/FF are characterized by a higher sensitivity and specificity compared to MD and FA in the discrimination between healthy, and osteoporotic subjects. MD/FF vs FA/FF graph extracted from femoral neck, identify all healthy individuals according to DXA results. CONCLUSION: DTI-(1)H-MRS protocol performed in femoral neck seems to be highly sensitive and specific in identifying healthy subjects. A MR exam is more expensive when compared to a DXA investigation. However, even though DXA BMD evaluation has been the accepted standard for osteoporosis diagnosis, DXA result has a low predictive value on patients' risk for future fractures. Thus, new approaches for examining patients at risk for developing osteoporosis would be desirable. Preliminary results showed here suggest that future studies on a larger population based on DTI assessment in the femoral neck, in combination with (1)H-MRS investigations, might allow screening of high-risk populations and the establishment of cut-off values of normality, with potential application of the method to single subjects

Apparent Diffusion Coefficient Assessment of Brain Development in Normal Fetuses and Ventriculomegaly

Diffusion neuro-MRI has benefited significantly from sophisticated pre-processing procedures aimed at improving image quality and diagnostic. In this work, diffusion-weighted imaging (DWI) was used with artifact correction and the apparent diffusion coefficient (ADC) was quantified to investigate fetal brain development. The DWI protocol was designed in order to limit the acquisition time and to estimate ADC without perfusion bias. The ADC in normal fetal brains was compared to cases with isolated ventriculomegaly (VM), a common fetal disease whose DWI studies are still scarce. DWI was performed in 58 singleton fetuses (Gestational age (GA) range: 19–38w) at 1.5T. In 31 cases, VM was diagnosed on ultrasound. DW-Spin Echo EPI with b-values = 50, 200, 700 s/mm2 along three orthogonal axes was used. All images were corrected for noise, Gibbs-ringing, and motion artifacts. The signal-to-noise ratio (SNR) was calculated and the ADC was measured with a linear least-squared algorithm. A multi-way ANOVA was used to evaluate differences in ADC between normal and VM cases and between second and third trimester in different brain regions. Correlation between ADC and GA was assessed with linear and quadratic regression analysis. Noise and artifact correction considerably increased SNR and the goodness-of-fit. ADC measurements were significantly different between second and third trimester in centrum semiovale, frontal white matter, thalamus, cerebellum and pons of both normal and VM brains (p ≤ 0.03). ADC values were significantly different between normal and VM in centrum semiovale and frontal white matter (p ≤ 0.02). ADC values in centrum semiovale, thalamus, cerebellum and pons linearly decreased with GA both in normal and VM brains, while a quadratic relation with GA was found in basal ganglia and occipital white matter of normal brains and in frontal white matter of VM (p ≤ 0.02). ADC values in all fetal brain regions were lower than those reported in literature where DWI with b = 0 was performed. Conversely, they were in agreement with the results of other authors who measured perfusion and diffusion contributions separately. By optimizing our DWI protocol we achieved an unbiased quantification of brain ADC in reasonable scan time. Our findings suggested that ADC can be a useful biomarker of brain abnormalities associated with VM

Apparent diffusion coefficient assessment of brain development in normal fetuses and ventriculomegaly

Diffusion neuro-MRI has benefited significantly from sophisticated pre-processing procedures aimed at improving image quality and diagnostic. In this work, diffusion-weighted imaging (DWI) was used with artifact correction and the apparent diffusion coefficient (ADC) was quantified to investigate fetal brain development. The DWI protocol was designed in order to limit the acquisition time and to estimate ADC without perfusion bias. The ADC in normal fetal brains was compared to cases with isolated ventriculomegaly (VM), a common fetal disease whose DWI studies are still scarce. DWI was performed in 58 singleton fetuses (Gestational age (GA) range: 19–38w) at 1.5T. In 31 cases, VM was diagnosed on ultrasound. DW-Spin Echo EPI with b-values = 50, 200, 700 s/mm2 along three orthogonal axes was used. All images were corrected for noise, Gibbs-ringing, and motion artifacts. The signal-to-noise ratio (SNR) was calculated and the ADC was measured with a linear least-squared algorithm. A multi-way ANOVA was used to evaluate differences in ADC between normal and VM cases and between second and third trimester in different brain regions. Correlation between ADC and GA was assessed with linear and quadratic regression analysis. Noise and artifact correction considerably increased SNR and the goodness-of-fit. ADC measurements were significantly different between second and third trimester in centrum semiovale, frontal white matter, thalamus, cerebellum and pons of both normal and VM brains (p ≤ 0.03). ADC values were significantly different between normal and VM in centrum semiovale and frontal white matter (p ≤ 0.02). ADC values in centrum semiovale, thalamus, cerebellum and pons linearly decreased with GA both in normal and VM brains, while a quadratic relation with GA was found in basal ganglia and occipital white matter of normal brains and in frontal white matter of VM (p ≤ 0.02). ADC values in all fetal brain regions were lower than those reported in literature where DWI with b = 0 was performed. Conversely, they were in agreement with the results of other authors who measured perfusion and diffusion contributions separately. By optimizing our DWI protocol we achieved an unbiased quantification of brain ADC in reasonable scan time. Our findings suggested that ADC can be a useful biomarker of brain abnormalities associated with VM

Simulating (electro)hydrodynamic effects in colloidal dispersions: smoothed profile method

Previously, we have proposed a direct simulation scheme for colloidal dispersions in a Newtonian solvent [Phys.Rev.E 71,036707 (2005)]. An improved formulation called the ``Smoothed Profile (SP) method'' is presented here in which simultaneous time-marching is used for the host fluid and colloids. The SP method is a direct numerical simulation of particulate flows and provides a coupling scheme between the continuum fluid dynamics and rigid-body dynamics through utilization of a smoothed profile for the colloidal particles. Moreover, the improved formulation includes an extension to incorporate multi-component fluids, allowing systems such as charged colloids in electrolyte solutions to be studied. The dynamics of the colloidal dispersions are solved with the same computational cost as required for solving non-particulate flows. Numerical results which assess the hydrodynamic interactions of colloidal dispersions are presented to validate the SP method. The SP method is not restricted to particular constitutive models of the host fluids and can hence be applied to colloidal dispersions in complex fluids

Fast algorithm for real-time rings reconstruction

The GAP project is dedicated to study the application of GPU in several contexts in which real-time response is important to take decisions. The definition of real-time depends on the application under study, ranging from answer time of μs up to several hours in case of very computing intensive task. During this conference we presented our work in low level triggers [1] [2] and high level triggers [3] in high energy physics experiments, and specific application for nuclear magnetic resonance (NMR) [4] [5] and cone-beam CT [6]. Apart from the study of dedicated solution to decrease the latency due to data transport and preparation, the computing algorithms play an essential role in any GPU application. In this contribution, we show an original algorithm developed for triggers application, to accelerate the ring reconstruction in RICH detector when it is not possible to have seeds for reconstruction from external trackers