Biological networks are characterized by their connectivity and topology but also by their ability to transport materials. In the case of random transportation, the efficacy is measured by the time it takes to travel between two nodes of the network. We study here the consequences of a unidirectional transport mechanism occurring in the endoplasmic reticulum (ER) network, a structure present in the cell cytoplasm. This unidirectional transport mechanism is an active-waiting transportation, where molecules have to wait a random time before being transported from one node to the next one. We develop here a general theory of transport in an active network and find an unusual network transportation, where molecules group together in redundant packets instead of being disperse. Finally, the mean time to travel between two nodes of the ER is of the order of 20 min, but is reduced to 30 s when we consider the fastest particles because it uses optimal paths. To conclude, the present theory shows that unidirectional transport is an efficient and robust mechanism for fast molecular redistribution inside the ER.

Objective: Electroencephalography (EEG) has become very common in clinical practice due to its relatively low cost, ease of installation, non-invasiveness, and good temporal resolution. Portable EEG devices are increasingly popular in clinical monitoring applications such as sleep scoring or anesthesia monitoring. In these situations, for reasons of speed and simplicity only few electrodes are used and contamination of the EEG signal by artifacts is inevitable. Visual inspection and manual removal of artifacts is often not possible, especially in real-time applications. Our goal is to develop a flexible technique to remove EEG artifacts in these contexts with minimal supervision. Methods: We propose here a new wavelet-based method which allows to remove artifacts from single-channel EEGs. The method is based on a datadriven renormalization of the wavelet components and is capable of adaptively attenuate artifacts of different nature. We benchmark our method against alternative artifact removal techniques. Results: We assessed the performance of the proposed method on publicly available datasets comprising ocular, muscular, and movement artifacts. The proposed method shows superior performances on different kinds of artifacts and signal-to-noise levels. Finally, we present an application of our method to the monitoring of general anesthesia. Conclusions: We show that our method can successfully attenuate various types of artifacts in single-channel EEG. Significance: Thanks to its data-driven approach and low computational cost, the proposed method provides a valuable tool to remove artifacts in real-time EEG applications with few electrodes, such as monitoring in special care units.