2,814 research outputs found
Graph theoretical analysis of complex networks in the brain
Since the discovery of small-world and scale-free networks the study of complex systems from a network perspective has taken an enormous flight. In recent years many important properties of complex networks have been delineated. In particular, significant progress has been made in understanding the relationship between the structural properties of networks and the nature of dynamics taking place on these networks. For instance, the 'synchronizability' of complex networks of coupled oscillators can be determined by graph spectral analysis. These developments in the theory of complex networks have inspired new applications in the field of neuroscience. Graph analysis has been used in the study of models of neural networks, anatomical connectivity, and functional connectivity based upon fMRI, EEG and MEG. These studies suggest that the human brain can be modelled as a complex network, and may have a small-world structure both at the level of anatomical as well as functional connectivity. This small-world structure is hypothesized to reflect an optimal situation associated with rapid synchronization and information transfer, minimal wiring costs, as well as a balance between local processing and global integration. The topological structure of functional networks is probably restrained by genetic and anatomical factors, but can be modified during tasks. There is also increasing evidence that various types of brain disease such as Alzheimer's disease, schizophrenia, brain tumours and epilepsy may be associated with deviations of the functional network topology from the optimal small-world pattern
Scattering matrices and expansion coefficients of Martian analogue palagonite particles
We present measurements of ratios of elements of the scattering matrix of
Martian analogue palagonite particles for scattering angles ranging from 3 to
174 degrees and a wavelength of 632.8 nm. To facilitate the use of these
measurements in radiative transfer calculations we have devised a method that
enables us to obtain, from these measurements, a normalized synthetic
scattering matrix covering the complete scattering angle range from 0 to 180
degrees. Our method is based on employing the coefficients of the expansions of
scattering matrix elements into generalized spherical functions. The synthetic
scattering matrix elements and/or the expansion coefficients obtained in this
way, can be used to include multiple scattering by these irregularly shaped
particles in (polarized) radiative transfer calculations, such as calculations
of sunlight that is scattered in the dusty Martian atmosphere.Comment: 34 pages 7 figures 1 tabl
Comparing Brain Networks of Different Size and Connectivity Density Using Graph Theory
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) non-significant (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 small-world index. To avoid such a bias we tried to estimate the N,k-dependence 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 here-investigated methods allows for a reliable and fully unbiased comparison, but some perform better than others
Test your surrogate data before you test for nonlinearity
The schemes for the generation of surrogate data in order to test the null
hypothesis of linear stochastic process undergoing nonlinear static transform
are investigated as to their consistency in representing the null hypothesis.
In particular, we pinpoint some important caveats of the prominent algorithm of
amplitude adjusted Fourier transform surrogates (AAFT) and compare it to the
iterated AAFT (IAAFT), which is more consistent in representing the null
hypothesis. It turns out that in many applications with real data the
inferences of nonlinearity after marginal rejection of the null hypothesis were
premature and have to be re-investigated taken into account the inaccuracies in
the AAFT algorithm, mainly concerning the mismatching of the linear
correlations. In order to deal with such inaccuracies we propose the use of
linear together with nonlinear polynomials as discriminating statistics. The
application of this setup to some well-known real data sets cautions against
the use of the AAFT algorithm.Comment: 14 pages, 15 figures, submitted to Physical Review
Gauge covariance and the fermion-photon vertex in three- and four- dimensional, massless quantum electrodynamics
In the quenched approximation, the gauge covariance properties of three
vertex Ans\"{a}tze in the Schwinger-Dyson equation for the fermion self energy
are analysed in three- and four- dimensional quantum electrodynamics. Based on
the Cornwall-Jackiw-Tomboulis effective action, it is inferred that the
spectral representation used for the vertex in the gauge technique cannot
support dynamical chiral symmetry breaking. A criterion for establishing
whether a given Ansatz can confer gauge covariance upon the Schwinger-Dyson
equation is presented and the Curtis and Pennington Ansatz is shown to satisfy
this constraint. We obtain an analytic solution of the Schwinger-Dyson equation
for quenched, massless three-dimensional quantum electrodynamics for arbitrary
values of the gauge parameter in the absence of dynamical chiral symmetry
breaking.Comment: 17 pages, PHY-7143-TH-93, REVTE
Localized energy for wave equations with degenerate trapping
Localized energy estimates have become a fundamental tool when studying wave
equations in the presence of asymptotically at background geometry. Trapped
rays necessitate a loss when compared to the estimate on Minkowski space. A
loss of regularity is a common way to incorporate such. When trapping is
sufficiently weak, a logarithmic loss of regularity suffices. Here, by studying
a warped product manifold introduced by Christianson and Wunsch, we encounter
the first explicit example of a situation where an estimate with an algebraic
loss of regularity exists and this loss is sharp. Due to the global-in-time
nature of the estimate for the wave equation, the situation is more complicated
than for the Schr\"{o}dinger equation. An initial estimate with sub-optimal
loss is first obtained, where extra care is required due to the low frequency
contributions. An improved estimate is then established using energy
functionals that are inspired by WKB analysis. Finally, it is shown that the
loss cannot be improved by any power by saturating the estimate with a
quasimode.Comment: 18 page
Real-time PCR reveals a high incidence of Symbiodinium clade D at low levels in four scleractinian corals across the Great Barrier Reef:Implications for symbiont shuffling
Reef corals form associations with an array of genetically and physiologically distinct endosymbionts from the genus Symbiodinium. Some corals harbor different clades of symbionts simultaneously, and over time the relative abundances of these clades may change through a process called symbiont shuffling. It is hypothesized that this process provides a mechanism for corals to respond to environmental threats such as global warming. However, only a minority of coral species have been found to harbor more than one symbiont clade simultaneously and the current view is that the potential for symbiont shuffling is limited. Using a newly developed real-time PCR assay, this paper demonstrates that previous studies have underestimated the presence of background symbionts because of the low sensitivity of the techniques used. The assay used here targets the multi-copy rDNA ITS1 region and is able to detect Symbiodinium clades C and D with > 100-fold higher sensitivity compared to conventional techniques. Technical considerations relating to intragenomic variation, estimating copy number and non-symbiotic contamination are discussed. Eighty-two colonies from four common scleractinian species (Acropora millepora, Acropora tenuis, Stylophora pistillata and Turbinaria reniformis) and 11 locations on the Great Barrier Reef were tested for background Symbiodinium clades. Although these colonies had been previously identified as harboring only a single clade based on SSCP analyses, background clades were detected in 78% of the samples, indicating that the potential for symbiont shuffling may be much larger than currently thought
Schwinger Model Green functions with topological effects
The fermion propagator and the 4-fermion Green function in the massless QED2
are explicitly found with topological effects taken into account. The
corrections due to instanton sectors k=+1,-1, contributing to the propagator,
are shown to be just the homogenous terms admitted by the Dyson-Schwinger
equation for S. In the case of the 4-fermion function also sectors k=+2,-2 are
included into consideration. The quark condensates are then calculated and are
shown to satisfy cluster property. The theta-dependence exhibited by the Green
functions corresponds to and may be removed by performing certain chiral gauge
transformation.Comment: 16 pages, in REVTE
MEG resting state functional connectivity in Parkinson's disease related dementia
Parkinson's disease (PD) related dementia (PDD) develops in up to 60% of patients, but the pathophysiology is far from being elucidated. Abnormalities of resting state functional connectivity have been reported in Alzheimer's disease (AD). The present study was performed to determine whether PDD is likewise characterized by changes in resting state functional connectivity. MEG recordings were obtained in 13 demented and 13 non-demented PD patients. The synchronization likelihood (SL) was calculated within and between cortical areas in six frequency bands. Compared to non-demented PD, PDD was characterized by lower fronto-temporal SL in the alpha range, lower intertemporal SL in delta, theta and alpha1 bands as well as decreased centro-parietal gamma band synchronization. In addition, higher parieto-occipital synchronization in the alpha2 and beta bands was found in PDD. The observed changes in functional connectivity are reminiscent of changes in AD, and may reflect reduced cholinergic activity and/or loss of cortico-cortical anatomical connections in PDD. © 2008 The Author(s)
Four-point Green functions in the Schwinger Model
The evaluation of the 4-point Green functions in the 1+1 Schwinger model is
presented both in momentum and coordinate space representations. The crucial
role in our calculations play two Ward identities: i) the standard one, and ii)
the chiral one. We demonstrate how the infinite set of Dyson-Schwinger
equations is simplified, and is so reduced, that a given n-point Green function
is expressed only through itself and lower ones. For the 4-point Green
function, with two bosonic and two fermionic external `legs', a compact
solution is given both in momentum and coordinate space representations. For
the 4-fermion Green function a selfconsistent equation is written down in the
momentum representation and a concrete solution is given in the coordinate
space. This exact solution is further analyzed and we show that it contains a
pole corresponding to the Schwinger boson. All detailed considerations given
for various 4-point Green functions are easily generizable to higher functions.Comment: In Revtex, 12 pages + 2 PostScript figure
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