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54
Comparing Brain Networks of Different Size and Connectivity Density Using Graph Theory
, 2009
"... Graph theory is a valuable framework to study the organization of functional and anatomical connections in the brain. Its use for comparing network topologies, however, is not without difficulties. Graph measures may be influenced by the number of nodes (N) and the average degree (k) of the network. ..."
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Graph theory is a valuable framework to study the organization of functional and anatomical connections in the brain. Its use for comparing network topologies, however, is not without difficulties. Graph measures may be influenced by the number of nodes (N) and the average degree (k) of the network. The explicit form of that influence depends on the type of network topology, which is usually unknown for experimental data. Direct comparisons of graph measures between empirical networks with different N and/or k can therefore yield spurious results. We list benefits and pitfalls of various approaches that intend to overcome these difficulties. We discuss the initial graph definition of unweighted graphs via fixed thresholds, average degrees or edge densities, and the use of weighted graphs. For instance, choosing a threshold to fix N and k does eliminate size and density effects but may lead to modifications of the network by enforcing (ignoring) nonsignificant (significant) connections. Opposed to fixing N and k, graph measures are often normalized via random surrogates but, in fact, this may even increase the sensitivity to differences in N and k for the commonly used clustering coefficient and smallworld index. To avoid such a bias we tried to estimate the N,kdependence for empirical networks, which can serve to correct for size effects, if successful. We also add a number of methods used in social sciences that build on statistics of local network structures including exponential random graph models and motif counting. We show that none of the hereinvestigated
POSTER PRESENTATION Open Access The effects of time delays on synchronization properties in a network of neural mass models
"... Patterns of (de)synchronization are key to neural functioning. We asked what general mechanisms are responsible for the emergence and disappearance of these (de) synchronization patterns. To answer this question we analytically revealed potential effects of physiologically motivated time delays in ..."
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Patterns of (de)synchronization are key to neural functioning. We asked what general mechanisms are responsible for the emergence and disappearance of these (de) synchronization patterns. To answer this question we analytically revealed potential effects of physiologically motivated time delays in neural populations. We investigated a network of Neural Mass Models (NMM), here Freeman’s seminal model that has successfully been used to model alphaoscillations [1] and EEG activity in the olfactory system [2] and visual cortex [3]. In contrast to these local applications we were interested in distributed activities over larger networks and hence coupled arbitrarily many NMMs involving the aforementioned time delays. That is, we represented activity in distinct brain areas by means of oscillatory excitatory/inhibitory
There’s no cloning in symplectic mechanics
, 2010
"... The fact that you can’t clone a quantum system is closely related to the fact that the tensor product in the category of Hilbert spaces is nonCartesian. At the end of his 2008 classical mechanics course, John Baez pointed out that the tensor product in the category of Poisson manifolds is also non ..."
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The fact that you can’t clone a quantum system is closely related to the fact that the tensor product in the category of Hilbert spaces is nonCartesian. At the end of his 2008 classical mechanics course, John Baez pointed out that the tensor product in the category of Poisson manifolds is also nonCartesian, which should mean there’s a classical analogue of the nocloning theorem [4]! This turns out to be true in symplectic mechanics, and I don’t see any reason it shouldn’t be true in more generalized settings as well. 1.2 Symplectic mechanics In symplectic mechanics, physical systems are represented by symplectic manifolds, and physical processes are represented by symplectomorphisms. If M and N are symplectic manifolds with symplectic forms ω and σ, respectively, the product manifold M × N has a natural symplectic form Ω given by Ω[(u, s), (v, t)] = ω(u, v) + σ(s, t), where u and v are tangent vectors at the same point in M, and s and t are tangent vectors at the same point in N [3, page 7]. I’ll denote the resulting symplectic manifold M ⊗ N to emphasize that it’s not a Cartesian product in the category of symplectic manifolds. I’ll often write a point in M ⊗ N as an ordered pair of points in M and N, just as I previously wrote a tangent vector on M ⊗ N as an ordered pair of tangent vectors on M and N. 2
DOI:10.1068/b2682 Selforganized settlements
, 1999
"... Abstract. In the present study we address the question of how persons or families occupy specific locations according to an attractiveness function between persons and flats. We suggest a mathematically formulated model in order to find optimal distributions of persons over flats. The model maximize ..."
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Abstract. In the present study we address the question of how persons or families occupy specific locations according to an attractiveness function between persons and flats. We suggest a mathematically formulated model in order to find optimal distributions of persons over flats. The model maximizes the global attractiveness of the ensemble and accounts for various conflicting situations. Its solutions show that, depending on initial conditions, both optimal as well as suboptimal configurations can be reached. An interpretation of the approach in terms of mental maps is offered. 1
RESEARCH ARTICLE How to Sync to the Beat of a Persistent Fractal Metronome without Falling Off the Treadmill?
"... In rehabilitation, rhythmic acoustic cues are often used to improve gait. However, stridetime fluctuations become antipersistent with such pacing, thereby deviating from the characteristic persistent longrange correlations in stride times of selfpaced walking healthy adults. Recent studies ther ..."
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In rehabilitation, rhythmic acoustic cues are often used to improve gait. However, stridetime fluctuations become antipersistent with such pacing, thereby deviating from the characteristic persistent longrange correlations in stride times of selfpaced walking healthy adults. Recent studies therefore experimented with metronomes with persistence in interbeat intervals and successfully evoked persistent stridetime fluctuations. The objective of this study was to examine how participants couple their gait to a persistent metronome, evoking persistently longer or shorter stride times over multiple consecutive strides, without wandering off the treadmill. Twelve healthy participants walked on a treadmill in selfpaced, isochronously paced and nonisochronously paced conditions, the latter with antipersistent, uncorrelated and persistent correlations in interbeat intervals. Stridetostride fluctuations of stride times, stride lengths and stride speeds were assessed with detrended fluctuation analysis, in conjunction with an examination of the coupling between stride times and stride lengths. Stridespeed fluctuations were antipersistent for all conditions. Stridetime and stridelength fluctuations were persistent for selfpaced walking and antipersistent
SEE PROFILE
, 2013
"... A benchmark test of accuracy and precision in estimating dynamical systems characteristics from a time series ..."
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A benchmark test of accuracy and precision in estimating dynamical systems characteristics from a time series
HUMAN NEUROSCIENCE Review Article
, 2010
"... doi: 10.3389/fnhum.2010.00209 Localizing and estimating causal relations of interacting brain rhythms ..."
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doi: 10.3389/fnhum.2010.00209 Localizing and estimating causal relations of interacting brain rhythms
BMC Neurology BioMed Central Study protocol Comparing unilateral and bilateral upper limb training: The ULTRAstroke program design
, 2009
"... This is an Open Access article distributed under the terms of the Creative Commons Attribution License ..."
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This is an Open Access article distributed under the terms of the Creative Commons Attribution License
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