Democracies at war Reiter, Dan; Stam, Allan C
2008., 20100701, 2010, 2002, 2002-01-01
eBook
Why do democracies win wars? This is a critical question in the study of international relations, as a traditional view--expressed most famously by Alexis de Tocqueville--has been that democracies ...are inferior in crafting foreign policy and fighting wars. In Democracies at War, the first major study of its kind, Dan Reiter and Allan Stam come to a very different conclusion. Democracies tend to win the wars they fight--specifically, about eighty percent of the time.
Many complex and interesting phenomena in nature are due to nonlinear phenomena. The theory of nonlinear dynamical systems, also called ‘chaos theory’, has now progressed to a stage, where it becomes ...possible to study self-organization and pattern formation in the complex neuronal networks of the brain. One approach to nonlinear time series analysis consists of reconstructing, from time series of EEG or MEG, an attractor of the underlying dynamical system, and characterizing it in terms of its dimension (an estimate of the degrees of freedom of the system), or its Lyapunov exponents and entropy (reflecting unpredictability of the dynamics due to the sensitive dependence on initial conditions). More recently developed nonlinear measures characterize other features of local brain dynamics (forecasting, time asymmetry, determinism) or the nonlinear synchronization between recordings from different brain regions.
Nonlinear time series has been applied to EEG and MEG of healthy subjects during no-task resting states, perceptual processing, performance of cognitive tasks and different sleep stages. Many pathologic states have been examined as well, ranging from toxic states, seizures, and psychiatric disorders to Alzheimer's, Parkinson's and Cre1utzfeldt-Jakob's disease. Interpretation of these results in terms of ‘functional sources’ and ‘functional networks’ allows the identification of three basic patterns of brain dynamics: (i) normal, ongoing dynamics during a no-task, resting state in healthy subjects; this state is characterized by a high dimensional complexity and a relatively low and fluctuating level of synchronization of the neuronal networks; (ii) hypersynchronous, highly nonlinear dynamics of epileptic seizures; (iii) dynamics of degenerative encephalopathies with an abnormally low level of between area synchronization. Only intermediate levels of rapidly fluctuating synchronization, possibly due to critical dynamics near a phase transition, are associated with normal information processing, whereas both hyper—as well as hyposynchronous states result in impaired information processing and disturbed consciousness.
Abstract The pathophysiological mechanisms underlying clinical symptoms in neurodegenerative disorders such as Parkinson's disease (PD) and Alzheimer's disease (AD) are incompletely understood. ...Magnetoencephalography (MEG) is a relatively new functional neuroimaging technique, which allows the simultaneous recording of the brain's magnetic activity from large arrays of sensors covering the whole head. MEG studies in PD and AD have identified characteristic patterns of abnormal oscillatory activity in different frequency bands. Furthermore, MEG studies aimed at the characterization of distributed functional networks have demonstrated distinct patterns of abnormal connectivity in demented and non-demented PD, as well as in AD. In PD abnormal oscillatory activity and disturbed connectivity may respond differently to dopaminergic treatment. Further studies in this field could benefit from new technological developments such as ultra low field MRI and from the application of a well-defined theoretical framework such as graph theory to the study of disturbed brain networks.
The brain is increasingly studied with graph theoretical approaches, which can be used to characterize network topology. However, studies on brain networks have reported contradictory findings, and ...do not easily converge to a clear concept of the structural and functional network organization of the brain. It has recently been suggested that the minimum spanning tree (MST) may help to increase comparability between studies. The MST is an acyclic sub-network that connects all nodes and may solve several methodological limitations of previous work, such as sensitivity to alterations in connection strength (for weighted networks) or link density (for unweighted networks), which may occur concomitantly with alterations in network topology under empirical conditions. If analysis of MSTs avoids these methodological limitations, understanding the relationship between MST characteristics and conventional network measures is crucial for interpreting MST brain network studies. Here, we firstly demonstrated that the MST is insensitive to alterations in connection strength or link density. We then explored the behavior of MST and conventional network-characteristics for simulated regular and scale-free networks that were gradually rewired to random networks. Surprisingly, although most connections are discarded during construction of the MST, MST characteristics were equally sensitive to alterations in network topology as the conventional graph theoretical measures. The MST characteristics diameter and leaf fraction were very strongly related to changes in the characteristic path length when the network changed from a regular to a random configuration. Similarly, MST degree, diameter, and leaf fraction were very strongly related to the degree of scale-free networks that were rewired to random networks. Analysis of the MST is especially suitable for the comparison of brain networks, as it avoids methodological biases. Even though the MST does not utilize all the connections in the network, it still provides a, mathematically defined and unbiased, sub-network with characteristics that can provide similar information about network topology as conventional graph measures.
•Conventional network analyses are accompanied with methodological limitations.•The minimum spanning tree is an acyclic sub-network that connects all nodes in the original network.•The minimum spanning tree avoids several methodological biases.•Minimum spanning tree metrics can be interpreted along the lines of conventional network analyses.
We investigated whether functional brain networks are abnormally organized in Alzheimer's disease (AD). To this end, graph theoretical analysis was applied to matrices of functional connectivity of ...beta band–filtered electroencephalography (EEG) channels, in 15 Alzheimer patients and 13 control subjects. Correlations between all pairwise combinations of EEG channels were determined with the synchronization likelihood. The resulting synchronization matrices were converted to graphs by applying a threshold, and cluster coefficients and path lengths were computed as a function of threshold or as a function of degree K. For a wide range of thresholds, the characteristic path length L was significantly longer in the Alzheimer patients, whereas the cluster coefficient C showed no significant changes. This pattern was still present when L and C were computed as a function of K. A longer path length with a relatively preserved cluster coefficient suggests a loss of complexity and a less optimal organization. The present study provides further support for the presence of “small-world” features in functional brain networks and demonstrates that AD is characterized by a loss of small-world network characteristics. Graph theoretical analysis may be a useful approach to study the complexity of patterns of interrelations between EEG channels.
A central question in modern neuroscience is how anatomical and functional connections between brain areas are organized to allow optimal information processing. In particular, both segregation and ...integration of information have to be dealt with in a single architecture of brain networks. There is strong evidence that synchronization of neural activity, both locally and between distant regions is a crucial code for functional interactions. However, a powerful theoretical framework to describe the structural and functional topology of system-wide brain networks has only become available with the discovery of ‘small-world’ and ‘scale-free’ networks in 1998 and 1999. There is now strong evidence that brain networks, ranging from simple nets of interconnected neurons up to macroscopic networks of brain areas display the typical features of complex systems: high clustering, short path lengths (both typical of ‘small-world’ networks), skewed degree distributions, presence of hubs, assortative mixing and the presence of modules. This has been demonstrated for anatomical and functional networks using neuroanatomical techniques, EEG, MEG and structural and functional MRI, in organisms ranging from C. elegans to man. In addition, network topology has been shown to be highly heritable, and very predictive of cognitive functioning. A short path length, which implies that from any area in the brain any other area can be reached in a small number of steps, is strongly correlated with IQ. Computational models are now beginning to reveal how the complex structure of adult brain networks could arise during development.
EEG and MEG (magnetoencephalography) are widely used to study functional connectivity between different brain regions. We address the question whether such connectivity patterns display an optimal ...organization for information processing. MEG recordings of five healthy human subjects were converted to sparsely connected graphs (
N=126;
k=15) by applying a suitable threshold to the
N∗
N matrix of synchronization strengths. For intermediate frequencies (8–30 Hz) the synchronization patterns were similar to those of an ordered graph with a consistent drop of synchronization strength as a function of distance. For low (<8 Hz) and high (>30 Hz) frequency bands the synchronization patterns displayed the features of a so-called ‘small-world’ network. This might reflect an optimal organization pattern for information processing, connecting any two brain area by only a small number of intermediate steps.
In recent years there has been a shift in focus from the study of local, mostly task-related activation to the exploration of the organization and functioning of large-scale structural and functional ...complex brain networks. Progress in the interdisciplinary field of modern network science has introduced many new concepts, analytical tools and models which allow a systematic interpretation of multivariate data obtained from structural and functional MRI, EEG and MEG. However, progress in this field has been hampered by the absence of a simple, unbiased method to represent the essential features of brain networks, and to compare these across different conditions, behavioural states and neuropsychiatric/neurological diseases. One promising solution to this problem is to represent brain networks by a minimum spanning tree (MST), a unique acyclic subgraph that connects all nodes and maximizes a property of interest such as synchronization between brain areas. We explain how the global and local properties of an MST can be characterized. We then review early and more recent applications of the MST to EEG and MEG in epilepsy, development, schizophrenia, brain tumours, multiple sclerosis and Parkinson's disease, and show how MST characterization performs compared to more conventional graph analysis. Finally, we illustrate how MST characterization allows representation of observed brain networks in a space of all possible tree configurations and discuss how this may simplify the construction of simple generative models of normal and abnormal brain network organization.
•Comparing brain networks is a challenge for modern network science.•The minimum spanning tree (MST) is a unique representation of weighted brain networks.•The MST reflects traffic flow and hierarchy in the underlying system.•MST sensitivity is comparable to classical graph theoretical brain network analysis.
Abstract Objective Neuronal networks with a so-called ‘small-world’ topography (characterized by strong clustering in combination with short path lengths) are known to facilitate synchronization, and ...possibly seizure generation. We tested the hypothesis that real functional brain networks during seizures display small-world features, using intracerebral recordings of mesial temporal lobe seizures. Methods We used synchronization likelihood (SL) to characterize synchronization patterns in intracerebral EEG recordings of 7 patients for 5 periods of interest: interictal, before-, during- and after rapid discharges (in which the last two periods are ictal) and postictal. For each period, graphs (abstract network representations) were reconstructed from the synchronization matrix and characterized by a clustering coefficient C (measure of local connectedness) and a shortest path length L (measure of overall network integration). Results were also compared with those obtained from random networks. Results The neuronal network changed during seizure activity, with an increase of C and L most prominent in the alpha, theta and delta frequency bands during and after the seizure. Conclusions During seizures, the neuronal network moves in the direction of a more ordered configuration (higher C combined with a slightly, but significantly, higher L ) compared to the more randomly organized interictal network, even after correcting for changes in synchronization strength. Significance Analysis of neuronal networks during seizures may provide insight into seizure genesis and development.
Ecological Stoichiometry theory predicts that the production, elemental structure and cellular content of biomolecules should depend on the relative availability of resources and the elemental ...composition of their producer organism. We review the extent to which carbon‐ and nitrogen‐rich phytoplankton toxins are regulated by nutrient limitation and cellular stoichiometry. Consistent with theory, we show that nitrogen limitation causes a reduction in the cellular quota of nitrogen‐rich toxins, while phosphorus limitation causes an increase in the most nitrogen‐rich paralytic shellfish poisoning toxin. In addition, we show that the cellular content of nitrogen‐rich toxins increases with increasing cellular N : P ratios. Also consistent with theory, limitation by either nitrogen or phosphorus promotes the C‐rich toxin cell quota or toxicity of phytoplankton cells. These observed relationships may assist in predicting and managing toxin‐producing phytoplankton blooms. Such a stoichiometric regulation of toxins is likely not restricted to phytoplankton, and may well apply to carbon‐ and nitrogen‐rich secondary metabolites produced by bacteria, fungi and plants.
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