Synchronous behavior in networks of coupled systems : with applications to neuronal dynamics

Synchronization in networks of interacting dynamical systems is an interesting phenomenon that arises in nature, science and engineering. Examples include the simultaneous flashing of thousands of fireflies, the synchronous firing of action potentials by groups of neurons, cooperative behavior of robots and synchronization of chaotic systems with applications to secure communication. How is it possible that systems in a network synchronize? A key ingredient is that the systems in the network "communicate" information about their state to the systems they are connected to. This exchange of information ultimately results in synchronization of the systems in the network. The question is how the systems in the network should be connected and respond to the received information to achieve synchronization. In other words, which network structures and what kind of coupling functions lead to synchronization of the systems? In addition, since the exchange of information is likely to take some time, can systems in networks show synchronous behavior in presence of time-delays? The first part of this thesis focusses on synchronization of identical systems that interact via diffusive coupling, that is a coupling defined through the weighted difference of the output signals of the systems. The coupling might contain timedelays. In particular, two types of diffusive time-delay coupling are considered: coupling type I is diffusive coupling in which only the transmitted signals contain a time-delay, and coupling type II is diffusive coupling in which every signal is timedelayed. It is proven that networks of diffusive time-delay coupled systems that satisfy a strict semipassivity property have solutions that are ultimately bounded. This means that the solutions of the interconnected systems always enter some compact set in finite time and remain in that set ever after. Moreover, it is proven that nonlinear minimum-phase strictly semipassive systems that interact via diffusive coupling always synchronize provided the interaction is sufficiently strong. If the coupling functions contain time-delays, then these systems synchronize if, in addition to the sufficiently strong interaction, the product of the time-delay and the coupling strength is sufficiently small. Next, the specific role of the topology of the network in relation to synchronization is discussed. First, using symmetries in the network, linear invariant manifolds for networks of the diffusively time-delayed coupled systems are identified. If such a linear invariant manifold is also attracting, then the network possibly shows partial synchronization. Partial synchronization is the phenomenon that some, at least two, systems in the network synchronize with each other but not with every system in the network. It is proven that a linear invariant manifold defined by a symmetry in a network of strictly semipassive systems is attracting if the coupling strength is sufficiently large and the product of the coupling strength and the time-delay is sufficiently small. The network shows partial synchronization if the values of the coupling strength and time-delay for which this manifold is attracting differ from those for which all systems in the network synchronize. Next, for systems that interact via symmetric coupling type II, it is shown that the values of the coupling strength and time-delay for which any network synchronizes can be determined from the structure of that network and the values of the coupling strength and time-delay for which two systems synchronize. In the second part of the thesis the theory presented in the first part is used to explain synchronization in networks of neurons that interact via electrical synapses. In particular, it is proven that four important models for neuronal activity, namely the Hodgkin-Huxley model, the Morris-Lecar model, the Hindmarsh-Rose model and the FitzHugh-Nagumo model, all have the semipassivity property. Since electrical synapses can be modeled by diffusive coupling, and all these neuronal models are nonlinear minimum-phase, synchronization in networks of these neurons happens if the interaction is sufficiently strong and the product of the time-delay and the coupling strength is sufficiently small. Numerical simulations with various networks of Hindmarsh-Rose neurons support this result. In addition to the results of numerical simulations, synchronization and partial synchronization is witnessed in an experimental setup with type II coupled electronic realizations of Hindmarsh-Rose neurons. These experimental results can be fully explained by the theoretical findings that are presented in the first part of the thesis. The thesis continues with a study of a network of pancreatic -cells. There is evidence that these beta-cells are diffusively coupled and that the synchronous bursting activity of the network is related to the secretion of insulin. However, if the network consists of active (oscillatory) beta-cells and inactive (dead) beta-cells, it might happen that, due to the interaction between the active and inactive cells, the activity of the network dies out which results in a inhibition of the insulin secretion. This problem is related to Diabetes Mellitus type 1. Whether the activity dies out or not depends on the number of cells that are active relative to the number of inactive cells. A bifurcation analysis gives estimates of the number of active cells relative to the number of inactive cells for which the network remains active. At last the controlled synchronization problem for all-to-all coupled strictly semipassive systems is considered. In particular, a systematic design procedure is presented which gives (nonlinear) coupling functions that guarantee synchronization of the systems. The coupling functions have the form of a definite integral of a scalar weight function on a interval defined by the outputs of the systems. The advantage of these coupling functions over linear diffusive coupling is that they provide high gain only when necessary, i.e. at those parts of the state space of the network where nonlinearities need to be suppressed. Numerical simulations in networks of Hindmarsh-Rose neurons support the theoretical results

Lyapunov-like Conditions of Forward Invariance and Boundedness for a Class of Unstable Systems

We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable subsystems with one-dimensional unstable dynamics or critically stable dynamics. Systems of this type arise in problems of nonlinear output regulation, parameter estimation and adaptive control. In addition to providing boundedness and convergence criteria the results allow to derive domains of initial conditions corresponding to solutions leaving a given neighborhood of the origin at least once. In contrast to other works addressing convergence issues in unstable systems, our results require neither input-output characterizations for the stable part nor estimates of convergence rates. The results are illustrated with examples, including the analysis of phase synchronization of neural oscillators with heterogenous coupling

Age-related microvascular degeneration in the human cerebral periventricular white matter

Clinical studies have identified white matter (WM) lesions as hyperintensive regions in the MRI images of elderly patients. Since a cerebrovascular origin was attributed to such lesions, the present analysis set out to define the microvascular histopathologic changes in the periventricular WM in the aged. Post-mortem samples of the frontal, parietal, and occipital periventricular WM of 40-90-year-old subjects were prepared for quantitative light and electron microscopy. Light microscopic examination revealed microvascular fibrohyalinosis as the most common type of microvascular damage in the elderly. Ultrastructural analysis identified the microvascular thickening as collagen deposits affecting the basement membrane. The vascular density did not correlate with the age. The basement membrane pathology significantly increased, while the number of intact microvessels gradually decreased, with advancing age in the frontal and occipital WM. Finally, peripheral atherosclerosis coincided with massive microvascular fibrosis, particularly in the frontal WM. Our results demonstrate an age-related microvascular degeneration in the periventricular WM, which may contribute to the development of WM lesions by hindering a sufficient supply of nutrients to the affected WM sites. Furthermore, the data accord with previous observations identifying the frontal lobe as the site at which WM vulnerability is most pronounced. Finally, atherosclerosis in large, peripheral vessels is considered to be a predictive marker of microvascular pathology in the WM.</p

Exploring community perceptions in preparation for a randomised controlled trial of biofortified flour in Pakistan

Background: Biofortification of staple food crops may be a cost-effective and sustainable approach to reducing micronutrient deficiencies in resource-poor settings with low dietary diversity. However, its success depends on uptake by the local population. This paper presents formative research conducted in a remote, rural community in North West Pakistan, prior to commencing a randomised controlled trial to test the effectiveness of consuming zinc-biofortified wheat flour for alleviating zinc deficiency. It explored local community members’ knowledge, understanding and attitudes towards biofortification and views on members of their community taking part in the trial. Methods: Four focus group discussions were conducted with male and female community members (separately for cultural reasons) and four in-depth interviews were conducted with Jirga members—respected male elders. Participation was limited to households that were ineligible for the trial so that we could explore the perspectives of community members who were not influenced by the incentives of the trial. Focus group participants were selected at community events for transparency. Data collection took place at the local school and homes of Jirga members. Thematic analysis was undertaken, using a combination of deductive and inductive approaches to identify key themes. Results: A total of 47 men and women participated in this study. Participants reported clear motivation to access and consume more nutritious flour, believing this would bring health benefits, particularly to women and children. Trusted members of the local community, including Jirga members and female health workers, should be involved in providing information on biofortified flour (and the trial) to increase levels of awareness and acceptance. Without their involvement, there is a risk that biofortified flour would be mistrusted. The cost of flour is the main factor affecting purchasing decisions, and biofortified flour will need to be cost-competitive to achieve widespread uptake in marginalised, rural communities. Conclusion: This formative study generated rich, qualitative data from a range of community stakeholders to improve the understanding of important barriers and facilitators to the widespread acceptability and adoption of biofortified wheat. Implementation research such as this will inform future decision-making in relation to scaling up biofortified wheat in Pakistan

Upstream sources of the Denmark Strait Overflow : observations from a high-resolution mooring array

© The Author(s), 2016. This is the author's version of the work and is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Deep Sea Research Part I: Oceanographic Research Papers 112 (2016): 94-112, doi:10.1016/j.dsr.2016.02.007.We present the first results from a densely instrumented mooring array upstream of the Denmark Strait sill, extending from the Iceland shelfbreak to the Greenland shelf. The array was deployed from September 2011 to July 2012, and captured the vast majority of overflow water denser than 27.8 kgm-3 approaching the sill. The mean transport of overflow water over the length of the deployment was 3.54 ± 0.16 Sv. Of this, 0.58 Sv originated from below sill depth, revealing that aspiration takes place in Denmark Strait. We confirm the presence of two main sources of overflow water: one approaching the sill in the East Greenland Current and the other via the North Icelandic Jet. Using an objective technique based on the hydrographic properties of the water, the transports of these two sources are found to be 2.54 ± 0.17 Sv and 1.00 ± 0.17 Sv, respectively. We further partition the East Greenland Current source into that carried by the shelfbreak jet (1.50 ± 0.16 Sv) versus that transported by a separated branch of the current on the Iceland slope (1.04 ± 0.15 Sv). Over the course of the year the total overflow transport is more consistent than the transport in either branch; compensation takes place among the pathways that maintains a stable total overflow transport. This is especially true for the two East Greenland Current branches whose transports vary out of phase with each other on weekly and longer time scales. We argue that wind forcing plays a role in this partitioning.The mooring and analysis work was supported by NSF OCE research grants OCE-0959381 and OCE-1433958, by the European Union 7th Framework Programme (FP7 2007-2013) under grant agreement n. 308299 NACLIM, and and by the Research Council of Norway through the Fram Centre Flaggship project 6606-299.2017-03-2

Upstream sources of the Denmark Strait Overflow : observations from a high-resolution mooring array

© The Author(s), 2016. This is the author's version of the work and is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Deep Sea Research Part I: Oceanographic Research Papers 112 (2016): 94-112, doi:10.1016/j.dsr.2016.02.007.We present the first results from a densely instrumented mooring array upstream of the Denmark Strait sill, extending from the Iceland shelfbreak to the Greenland shelf. The array was deployed from September 2011 to July 2012, and captured the vast majority of overflow water denser than 27.8 kgm-3 approaching the sill. The mean transport of overflow water over the length of the deployment was 3.54 ± 0.16 Sv. Of this, 0.58 Sv originated from below sill depth, revealing that aspiration takes place in Denmark Strait. We confirm the presence of two main sources of overflow water: one approaching the sill in the East Greenland Current and the other via the North Icelandic Jet. Using an objective technique based on the hydrographic properties of the water, the transports of these two sources are found to be 2.54 ± 0.17 Sv and 1.00 ± 0.17 Sv, respectively. We further partition the East Greenland Current source into that carried by the shelfbreak jet (1.50 ± 0.16 Sv) versus that transported by a separated branch of the current on the Iceland slope (1.04 ± 0.15 Sv). Over the course of the year the total overflow transport is more consistent than the transport in either branch; compensation takes place among the pathways that maintains a stable total overflow transport. This is especially true for the two East Greenland Current branches whose transports vary out of phase with each other on weekly and longer time scales. We argue that wind forcing plays a role in this partitioning.The mooring and analysis work was supported by NSF OCE research grants OCE-0959381 and OCE-1433958, by the European Union 7th Framework Programme (FP7 2007-2013) under grant agreement n. 308299 NACLIM, and and by the Research Council of Norway through the Fram Centre Flaggship project 6606-299.2017-03-2

The impact of maintenance therapy on sleep-wake rhythms and cancer-related fatigue in pediatric acute lymphoblastic leukemia

Purpose: To assess the impact of maintenance therapy and the additional impact of dexamethasone treatment on cancer-related fatigue and sleep-wake rhythms in pediatric acute lymphoblastic leukemia (ALL) patients and to determine the association between these outcomes. Methods: A national cohort of pediatric ALL patients (≥ 2 years) was included (± 1 year post-diagnosis). Patients receiving dexamethasone were assessed twice (assessment with and without dexamethasone). Actigraphy assessments were used to calculate sleep-wake outcomes with nonparametric methods. Cancer-related fatigue was assessed with the PedsQL Multidimensional Fatigue Scale. Sleep-wake rhythms and cancer-related fatigue were compared between patients participating in the assessment without dexamethasone and healthy children (linear regression) and between assessments with and without dexamethasone (mixed models). Using linear regression, associations between sleep-wake outcomes and cancer-related fatigue were determined during assessments with and without dexamethasone. Results: Responses were collected for 125 patients (113 assessments with and 81 without dexamethasone). The sleep-wake rhythm was less stable (p = 0.03) and less robust (p = 0.01), with lower physical activity l

The effect of aspirin and nonsteroidal anti-inflammatory drug use after diagnosis on survival of oesophageal cancer patients

Background:Aspirin use has been shown to lower incidence and mortality in cancer patients. The aim of this population-based study was to determine the effect of postdiagnosis low-dose aspirin use on survival of patients with oesophageal cancer.Methods:Patients with oesophageal cancer (1998-2010) were selected from the Eindhoven Cancer Registry and linked with outpatient pharmacy data regarding aspirin and nonsteroidal anti-inflammatory drugs (NSAIDs). Users were subdivided into both prediagnosis and postdiagnosis or only postdiagnosis users. Parametric survival models with an exponential (Poisson) distribution were used with non-specific death as endpoint.Results:In this study 560 patients were included. Overall, 157 patients (28.0%) were non-users, 293 patients (52.3%) pre-and postdiagnosis (89 aspirin and 204 NSAID users) and 110 patients (19.6%) only postdiagnosis users (16 aspirin and 94 NSAID users). Postdiagnosis aspirin use was associated with overall survival (RR 0.45 (95% CI 0.34-0.60; P<0.001); adjusted rat