Classification of streamflow hydrographs plays an important role in a large number of hydrological and hydraulic studies. For instance, it allows decisions to be made regarding the implementation of hydraulic structures and characterization of different flood types, leading to a better understanding of extreme flow behavior. The employed hydrograph classification methods are generally based on a finite number of hydrograph characteristics and do not include all the available information contained in a discharge time series. In this paper, two statistical techniques from the theory of functional data classification are adapted and applied for the analysis of flood hydrographs. Functional classification directly employs all data of a discharge time series and thus contains all available information on shape, peak, and timing. This potentially allows a better understanding and treatment of floods as well as other hydrological phenomena. The considered functional methodology is applied to streamflow datasets from the province of Quebec, Canada. It is shown that classes obtained using functional approaches have merit and can lead to better representation than those obtained using a multidimensional hierarchical classification method. The considered methodology has the advantage of using all of the information contained in the hydrograph, thus reducing the subjectivity that is inherent in multidimensional analysis of the type and number of characteristics to be used and consequently diminishing the associated uncertainty.

BACKGROUND AND PURPOSE: Objective and quantitative data to define cerebellar vermis and/or brain stem hypoplasia in children are lacking. Our aim was to provide MR imaging biometric references for the cerebellar vermis and brain stem from a large cohort of children with normal cerebellums. MATERIALS AND METHODS: The MR imaging data were retrospectively selected from our hospital data base from January 1, 2014, to December 31, 2017. All MR imaging examinations of children between 1 day and 15 years of age, including midline sagittal sections, were included. Children with a clinical history or MR imaging abnormalities that may affect the posterior fossa were excluded. We manually measured four 2D parameters: vermian height, anterior-posterior diameter of the vermis, anterior-posterior diameter of the midbrain-pons junction, and anterior-posterior midpons diameter. The inter- and intraobserver agreement was evaluated. RESULTS: Seven hundred eighteen children were included (372 boys and 346 girls), from 1 day to 15 years of age. Normal values (third to 97th percentiles) were provided for each parameter. The vermis parameters showed a rapid growth phase during the first year, a slower growth until the fifth year, and finally a near-plateau phase. The brain stem parameters showed more progressive growth. The intra- and interobserver agreement was excellent for all parameters. CONCLUSIONS: We provide reference biometric data of the vermis and the brain stem using simple and reproducible measurements that are easy to use in daily practice. The relevance of these 2D measurements should be further validated in diseases associated with cerebellar abnormalities.

This paper investigates a nonparametric spatial predictor of a stationary multidimensional spatial process observed over a rectangular domain. The proposed predictor depends on two kernels in order to control both the distance between observations and that between spatial locations. The uniform almost complete consistency and the asymptotic normality of the kernel predictor are obtained when the sample considered is an alpha-mixing sequence. Numerical studies were carried out in order to illustrate the behaviour of our methodology both for simulated data and for an environmental data set.