Manifold-adaptive dimension estimation revisited.

Data dimensionality informs us about data complexity and sets limit on the structure of successful signal processing pipelines. In this work we revisit and improve the manifold adaptive Farahmand-Szepesvári-Audibert (FSA) dimension estimator, making it one of the best nearest neighbor-based dimension estimators available. We compute the probability density function of local FSA estimates, if the local manifold density is uniform. Based on the probability density function, we propose to use the median of local estimates as a basic global measure of intrinsic dimensionality, and we demonstrate the advantages of this asymptotically unbiased estimator over the previously proposed statistics: the mode and the mean. Additionally, from the probability density function, we derive the maximum likelihood formula for global intrinsic dimensionality, if i.i.d. holds. We tackle edge and finite-sample effects with an exponential correction formula, calibrated on hypercube datasets. We compare the performance of the corrected median-FSA estimator with kNN estimators: maximum likelihood (Levina-Bickel), the 2NN and two implementations of DANCo (R and MATLAB). We show that corrected median-FSA estimator beats the maximum likelihood estimator and it is on equal footing with DANCo for standard synthetic benchmarks according to mean percentage error and error rate metrics. With the median-FSA algorithm, we reveal diverse changes in the neural dynamics while resting state and during epileptic seizures. We identify brain areas with lower-dimensional dynamics that are possible causal sources and candidates for being seizure onset zones.

Contemporary radiosurgery of cerebral cavernous malformations: Part 2. Treatment outcome for hemispheric lesions.

OBJECTIVEThe role of radiosurgery (RS) in treating superficial cavernous malformations (CMs) is insufficiently studied in part because of the disappointing results of early experimental attempts as compared to the mostly safe and effective microsurgery. Nonetheless, because of lesion- or treatment-specific factors, a therapeutic alternative may be required. In this study, the authors aimed to assess the safety of RS in treating superficial CMs and to analyze its long-term effect on hemorrhage rates and epilepsy control.METHODSThe authors conducted a retrospective analysis of 96 patients with 109 CMs located in the cerebral or cerebellar hemispheres and treated with RS between 1995 and 2014. A median of 15 Gy (range 10-25 Gy) was given to the 50% prescription isodose level, lesion volume was 604 mm3 (4-8300 mm3), and the prescription isodose volume was 638.5 mm3 (4-9500 mm3). Outcomes were compared to those of 206 deep-seated lesions reported on in another study. Ninety-five patients had available follow-up, which was a median of 7 years (1-21 years). Median patient age was 42 years (0.5-77) at presentation and 45 (3-80) at treatment. Seventy-one CMs presented with symptomatic hemorrhage, and 52 caused seizures.RESULTSIn the nonhemorrhagic group (37 lesions), one bleed occurred during the follow-up period, for an annual bleed rate of 0.4% per lesion. The lifetime annual bleed rate of CMs having a single hemorrhage prior to treatment was 2.5%. The rebleed rate in the single-bleed group decreased from 1.8% within the first 2 years after RS to 0.7% thereafter. The pretreatment rebleed rate for lesions having multiple bleeds prior to RS was 14.15%, which fell to 3.85% for the first 2 years after RS and declined to 1.3% thereafter. Multivariate analysis showed younger age, deep lesion location, and multiple pretreatment hemorrhages as significant predictors of posttreatment hemorrhage.Pretreatment hemorrhages led to permanent deficits in 41.4% of the cases with a single bleed and in 46.1% of cases with multiple bleeds. Only mild (modified Rankin Scale score 1) and a low rate of permanent neurological deficits were caused either by posttreatment hemorrhages (4.3%) or by radiation (2%).The rate of improvement in epilepsy was 84.9% after RS in patients with at least one seizure prior to treatment, not depending on the presence of hemorrhage or the time interval between presentation and treatment. Favorable outcome occurred in 81% of patients whose seizures were not controlled with antiepileptic medication prior to RS.CONCLUSIONSRadiosurgery for superficial CMs is safe and appears to be effective, offering a real treatment alternative to surgery for selected patients. Given their relatively benign natural history, superficial CMs require further study to verify the long-term benefit of RS over the lesions' natural history.