Objectives To assess the role of fetal magnetic resonance imaging (MRI) in detecting associated anomalies in fetuses presenting with mild or moderate isolated ventriculomegaly (VM) undergoing multiplanar ultrasound evaluation of the fetal brain. Methods This was a multicenter, retrospective, cohort study involving 15 referral fetal medicine centers in Italy, the UK and Spain. Inclusion criteria were fetuses affected by isolated mild (ventricular atrial diameter, 10.0–11.9 mm) or moderate (ventricular atrial diameter, 12.0–14.9 mm) VM on ultrasound, defined as VM with normal karyotype and no other additional central nervous system (CNS) or extra‐CNS anomalies on ultrasound, undergoing detailed assessment of the fetal brain using a multiplanar approach as suggested by the International Society of Ultrasound in Obstetrics and Gynecology guidelines for the fetal neurosonogram, followed by fetal MRI. The primary outcome of the study was to report the incidence of additional CNS anomalies detected exclusively on prenatal MRI and missed on ultrasound, while the secondary aim was to estimate the incidence of additional anomalies detected exclusively after birth and missed on prenatal imaging (ultrasound and MRI). Subgroup analysis according to gestational age at MRI (< 24 vs ≥ 24 weeks), laterality of VM (unilateral vs bilateral) and severity of dilatation (mild vs moderate VM) were also performed. Results Five hundred and fifty‐six fetuses with a prenatal diagnosis of isolated mild or moderate VM on ultrasound were included in the analysis. Additional structural anomalies were detected on prenatal MRI and missed on ultrasound in 5.4% (95% CI, 3.8–7.6%) of cases. When considering the type of anomaly, supratentorial intracranial hemorrhage was detected on MRI in 26.7% of fetuses, while polymicrogyria and lissencephaly were detected in 20.0% and 13.3% of cases, respectively. Hypoplasia of the corpus callosum was detected on MRI in 6.7% of cases, while dysgenesis was detected in 3.3%. Fetuses with an associated anomaly detected only on MRI were more likely to have moderate than mild VM (60.0% vs 17.7%; P < 0.001), while there was no significant difference in the proportion of cases with bilateral VM between the two groups (P = 0.2). Logistic regression analysis showed that lower maternal body mass index (adjusted odds ratio (aOR), 0.85 (95% CI, 0.7–0.99); P = 0.030), the presence of moderate VM (aOR, 5.8 (95% CI, 2.6–13.4); P < 0.001) and gestational age at MRI ≥ 24 weeks (aOR, 4.1 (95% CI, 1.1–15.3); P = 0.038) were associated independently with the probability of detecting an associated anomaly on MRI. Associated anomalies were detected exclusively at birth and missed on prenatal imaging in 3.8% of cases. Conclusions The incidence of an associated fetal anomaly missed on ultrasound and detected only on fetal MRI in fetuses with isolated mild or moderate VM undergoing neurosonography is lower than that reported previously. The large majority of these anomalies are difficult to detect on ultrasound. The findings fr...

Applications of optimal transport have recently gained remarkable attention thanks to the computational advantages of entropic regularization. However, in most situations the Sinkhorn approximation of the Wasserstein distance is replaced by a regularized version that is less accurate but easy to differentiate. In this work we characterize the differential properties of the original Sinkhorn distance, proving that it enjoys the same smoothness as its regularized version and we explicitly provide an efficient algorithm to compute its gradient. We show that this result benefits both theory and applications: on one hand, high order smoothness confers statistical guarantees to learning with Wasserstein approximations. On the other hand, the gradient formula allows us to efficiently solve learning and optimization problems in practice. Promising preliminary experiments complement our analysis.

We illustrate some novel contraction and regularizing properties of the Heat flow in metric-measure spaces that emphasize an interplay between Hellinger-Kakutani, Kantorovich-Wasserstein and Hellinger-Kantorvich distances. Contraction properties of Hellinger-Kakutani distances and general Csiszár divergences hold in arbitrary metric-measure spaces and do not require assumptions on the linearity of the flow.When weaker transport distances are involved, we will show that contraction and regularizing effects rely on the dual formulations of the distances and are strictly related to lower Ricci curvature bounds in the setting of RCD(K, ∞) metric measure spaces. Contents2010 Mathematics Subject Classification. Primary: 49Q20, 47D07; Secondary: 30L99.

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We present a novel algorithm to estimate the barycenter of arbitrary probability distributions with respect to the Sinkhorn divergence. Based on a Frank-Wolfe optimization strategy, our approach proceeds by populating the support of the barycenter incrementally, without requiring any pre-allocation. We consider discrete as well as continuous distributions, proving convergence rates of the proposed algorithm in both settings. Key elements of our analysis are a new result showing that the Sinkhorn divergence on compact domains has Lipschitz continuous gradient with respect to the Total Variation and a characterization of the sample complexity of Sinkhorn potentials. Experiments validate the effectiveness of our method in practice.