On a generalization of u

In this paper we present an extension of Bauer's work about u-means. We consider a kind of composition of an admissible function u(x) (described by Bauer) and of a compatible function ϕ(x). This construction allows us to define (u,ϕ)-means. When ϕ(x)=x, the (u,ϕ)-means are the u-means introduced by Bauer. The arithmetic, geometric and harmonic means are special cases

Probabilistic functional tractography of the human cortex revisited

In patients with pharmaco-resistant focal epilepsies investigated with intracranial electroencephalography (iEEG), direct electrical stimulations of a cortical region induce cortico-cortical evoked potentials (CCEP) in distant cerebral cortex, which properties can be used to infer large scale brain connectivity. In 2013, we proposed a new probabilistic functional tractography methodology to study human brain connectivity. We have now been revisiting this method in the F-TRACT project (f-tract.eu) by developing a large multicenter CCEP database of several thousand stimulation runs performed in several hundred patients, and associated processing tools to create a probabilistic atlas of human cortico-cortical connections. Here, we wish to present a snapshot of the methods and data of F-TRACT using a pool of 213 epilepsy patients, all studied by stereo-encephalography with intracerebral depth electrodes. The CCEPs were processed using an automated pipeline with the following consecutive steps: detection of each stimulation run from stimulation artifacts in raw intracranial EEG (iEEG) files, bad channels detection with a machine learning approach, model-based stimulation artifact correction, robust averaging over stimulation pulses. Effective connectivity between the stimulated and recording areas is then inferred from the properties of the first CCEP component, i.e. onset and peak latency, amplitude, duration and integral of the significant part. Finally, group statistics of CCEP features are implemented for each brain parcel explored by iEEG electrodes. The localization (coordinates, white/gray matter relative positioning) of electrode contacts were obtained from imaging data (anatomical MRI or CT scans before and after electrodes implantation). The iEEG contacts were repositioned in different brain parcellations from the segmentation of patients' anatomical MRI or from templates in the MNI coordinate system. The F-TRACT database using the first pool of 213 patients provided connectivity probability values for 95% of possible intrahemispheric and 56% of interhemispheric connections and CCEP features for 78% of intrahemisheric and 14% of interhemispheric connections. In this report, we show some examples of anatomo-functional connectivity matrices, and associated directional maps. We also indicate how CCEP features, especially latencies, are related to spatial distances, and allow estimating the velocity distribution of neuronal signals at a large scale. Finally, we describe the impact on the estimated connectivity of the stimulation charge and of the contact localization according to the white or gray matter. The most relevant maps for the scientific community are available for download on f-tract. eu (David et al., 2017) and will be regularly updated during the following months with the addition of more data in the F-TRACT database. This will provide an unprecedented knowledge on the dynamical properties of large fiber tracts in human.Peer reviewe

Growth models with oblique asymptote

A class of smooth functions which can be used as regression models for modelling phenomena requiring an oblique asymptote is analyzed. These types of models were defined as a product of a linear function and some well known growth models. In addition to their increasing character with an oblique asymptote, the resulting models provide curves with a single inflection point

Linear and logistic models with time dependent coefficients

We sutdy the effects of some properties of the carrying capacity on the solution of the linear and logistic differential equations. We present results concerning the behaviour and the asymptotic behaviour of their solutions. Special attention is paid when the carrying capacity is an increasing or a decreasing positive function. For more general carrying capacity, we obtain bounds for the corresponding solution by constructing appropriate subsolution and supersolution. We also present a decomposition of the solution of the linear, and logistic, differential equation as a product of the carrying capacity and the solution to the corresponding differential equation with a constant carrying capacity

GROWTH MODELS WITH OBLIQUE ASYMPTOTE

A class of smooth functions which can be used as regression models for modelling phenomena requiring an oblique asymptote is analyzed. These types of models were defined as a product of a linear function and some well known growth models. In addition to their increasing character with an oblique asymptote, the resulting models provide curves with a single inflection point

Long-term efficacy and safety of piracetam in the treatment of progressive myoclonus epilepsy

Background: Piracetam has been proven to be effective and well tolerated in the treatment of myoclonus in short-term studies

Réduction de l'excrétion de phosphore et d'azote chez le porc charcutier par l'ajout d'un objectif environnemental dans l'algorithme traditionnel de formulation

National audienc