Stationary states in random walks on networks

In this thesis we dealt with the problem of describing a transportation network in which the objects in movement were subject to both finite transportation capacity and finite accomodation capacity. The movements across such a system are realistically of a simultaneous nature which poses some challenges when formulating a mathematical description. We tried to derive such a general modellization from one posed on a simplified problem based on asyncronicity in particle transitions. We did so considering one-step processes based on the assumption that the system could be describable through discrete time Markov processes with finite state space. After describing the pre-established dynamics in terms of master equations we determined stationary states for the considered processes. Numerical simulations then led to the conclusion that a general system naturally evolves toward a congestion state when its particle transition simultaneously and we consider one single constraint in the form of network node capacity. Moreover the congested nodes of a system tend to be located in adjacent spots in the network, thus forming local clusters of congested nodes.

Nonrandomness, nonlinear dependence, and nonstationarity of electroencephalographic recordings from epilepsy patients

To derive tests for randomness, nonlinear-independence, and stationarity, we combine surrogates with a nonlinear prediction error, a nonlinear interdependence measure, and linear variability measures, respectively. We apply these tests to intracranial electroencephalographic recordings (EEG) from patients suffering from pharmacoresistant focal-onset epilepsy. These recordings had been performed prior to and independent from our study as part of the epilepsy diagnostics. The clinical purpose of these recordings was to delineate the brain areas to be surgically removed in each individual patient in order to achieve seizure control. This allowed us to define two distinct sets of signals: One set of signals recorded from brain areas where the first ictal EEG signal changes were detected as judged by expert visual inspection ("focal signals") and one set of signals recorded from brain areas that were not involved at seizure onset ("nonfocal signals"). We find more rejections for both the randomness and the nonlinear-independence test for focal versus nonfocal signals. In contrast more rejections of the stationarity test are found for nonfocal signals. Furthermore, while for nonfocal signals the rejection of the stationarity test increases the rejection probability of the randomness and nonlinear-independence test substantially, we find a much weaker influence for the focal signals. In consequence, the contrast between the focal and nonfocal signals obtained from the randomness and nonlinear-independence test is further enhanced when we exclude signals for which the stationarity test is rejected. To study the dependence between the randomness and nonlinear-independence test we include only focal signals for which the stationarity test is not rejected. We show that the rejection of these two tests correlates across signals. The rejection of either test is, however, neither necessary nor sufficient for the rejection of the other test. Thus, our results suggest that EEG signals from epileptogenic brain areas are less random, more nonlinear-dependent, and more stationary compared to signals recorded from nonepileptogenic brain areas. We provide the data, source code, and detailed results in the public domain.

Differential modulation of ROS signals and other mitochondrial parameters by the antioxidants MitoQ, resveratrol and curcumin in human adipocytes

Abstract Mitochondrial reactive oxygen species (ROS) have been demonstrated to play an important role as signaling and regulating molecules in human adipocytes. In order to evaluate the differential modulating roles of antioxidants, we treated human adipocytes differentiated from human bone marrow-derived mesenchymal stem cells with MitoQ, resveratrol and curcumin. The effects on ROS, viability, mitochondrial respiration and intracellular ATP levels were examined. MitoQ lowered both oxidizing and reducing ROS. Resveratrol decreased reducing and curcumin oxidizing radicals only. All three substances slightly decreased state III respiration immediately after addition. After 24 h of treatment, MitoQ inhibited both basal and uncoupled oxygen consumption, whereas curcumin and resveratrol had no effect. Intracellular ATP levels were not altered. This demonstrates that MitoQ, resveratrol and curcumin exert potent modulating effects on ROS signaling in human adipocyte with marginal effects on metabolic parameters.