1,228 research outputs found
Canonical Cortical Field Theories
We characterise the dynamics of neuronal activity, in terms of field theory,
using neural units placed on a 2D-lattice modelling the cortical surface. The
electrical activity of neuronal units was analysed with the aim of deriving a
neural field model with a simple functional form that still able to predict or
reproduce empirical findings. Each neural unit was modelled using a neural mass
and the accompanying field theory was derived in the continuum limit. The field
theory comprised coupled (real) Klein-Gordon fields, where predictions of the
model fall within the range of experimental findings. These predictions
included the frequency spectrum of electric activity measured from the cortex,
which was derived using an equipartition of energy over eigenfunctions of the
neural fields. Moreover, the neural field model was invariant, within a set of
parameters, to the dynamical system used to model each neuronal mass.
Specifically, topologically equivalent dynamical systems resulted in the same
neural field model when connected in a lattice; indicating that the fields
derived could be read as a canonical cortical field theory. We specifically
investigated non-dispersive fields that provide a structure for the coding (or
representation) of afferent information. Further elaboration of the ensuing
neural field theory, including the effect of dispersive forces, could be of
importance in the understanding of the cortical processing of information.Comment: 19 pages, 1 figur
Weak Lensing of the CMB: Cumulants of the Probability Distribution Function
We discuss the real-space moments of temperature anisotropies in the cosmic
microwave background (CMB) due to weak gravitational lensing by intervening
large-scale structure. We show that if the probability distribution function of
primordial temperature anisotropies is Gaussian, then it remains unchanged
after gravitational lensing. With finite resolution, however, non-zero
higher-order cumulants are generated both by lensing autocorrelations and by
cross-correlations between the lensing potential and secondary anisotropies in
the CMB such as the Sunayev-Zel'dovich (SZ) effect. Skewness is produced by
these lensing-SZ correlations, while kurtosis receives contributions from both
lensing alone and lensing-SZ correlations. We show that if the projected
lensing potential is Gaussian, all cumulants of higher-order than the kurtosis
vanish. While recent results raise the possibility of detection of the skewness
in upcoming data, the kurtosis will likely remain undetected.Comment: 11 pages, 4 figures, submitted to PR
Solar System: Sifting through the debris
A quadrillion previously unnoticed small bodies beyond Neptune have been
spotted as they dimmed X-rays from a distant source. Models of the dynamics of
debris in the Solar System's suburbs must now be reworked.Comment: 3 pages, 1 figure; Nature News and Views on Chang et al. 2006,
Nature, 442, 660-66
A Lensing Reconstruction of Primordial Cosmic Microwave Background Polarization
We discuss a possibility to directly reconstruct the CMB polarization field
at the last scattering surface by accounting for modifications imposed by the
gravitational lensing effect. The suggested method requires a tracer field of
the large scale structure lensing potentials that deflected propagating CMB
photons from the last scattering surface. This required information can come
from a variety of observations on the large scale structure matter
distribution, including convergence reconstructed from lensing shear studies
involving galaxy shapes. In the case of so-called curl, or B,-modes of CMB
polarization, the reconstruction allows one to identify the distinct signature
of inflationary gravitational waves.Comment: 6 pages, 2 figures; PRD submitte
Linear theory and velocity correlations of clusters
Linear theory provides a reasonable description of the velocity correlations
of biased tracers both perpendicular and parallel to the line of separation,
provided one accounts for the fact that the measurement is almost always made
using pair-weighted statistics. This introduces an additional term which, for
sufficiently biased tracers, may be large. Previous work suggesting that linear
theory was grossly in error for the components parallel to the line of
separation ignored this term.Comment: 5 pages, 2 figures, MNRAS accepte
A massive, distant proto-cluster at z=2.47 caught in a phase of rapid formation?
Numerical simulations of cosmological structure formation show that the
Universe's most massive clusters, and the galaxies living in those clusters,
assemble rapidly at early times (2.5 < z < 4). While more than twenty
proto-clusters have been observed at z > 2 based on associations of 5-40
galaxies around rare sources, the observational evidence for rapid cluster
formation is weak. Here we report observations of an asymmetric, filamentary
structure at z = 2.47 containing seven starbursting, submillimeter-luminous
galaxies and five additional AGN within a comoving volume of 15000 Mpc.
As the expected lifetime of both the luminous AGN and starburst phase of a
galaxy is ~100 Myr, we conclude that these sources were likely triggered in
rapid succession by environmental factors, or, alternatively, the duration of
these cosmologically rare phenomena is much longer than prior direct
measurements suggest. The stellar mass already built up in the structure is
and we estimate that the cluster mass will exceed that
of the Coma supercluster at . The filamentary structure is in line
with hierarchical growth simulations which predict that the peak of cluster
activity occurs rapidly at z > 2.Comment: 7 pages, 3 figures, 2 tables, accepted in ApJL (small revisions from
previous version
Geometrical tests of cosmological models. II. Calibration of rotational widths and disc scaling relations
This series of papers is dedicated to a new technique to select galaxies that
can act as standard rods and standard candles in order to perform geometrical
tests on large samples of high redshift galaxies to constrain different
cosmological parameters. The goals of this paper are (1) to compare different
rotation indicators in order to understand the relation between rotation
velocities extracted from observations of the Halpha line and the [OII]3727
line, and (2) determine the scaling relations between physical size, surface
brightness and magnitude of galaxies and their rotation velocity using the
SFI++, a large catalog of nearby galaxies observed at I-band. A good
correlation is observed between the rotation curve-derived velocities of the
Halpha and [OII] observations, as well as between those calculated from
velocity histograms, justifying the direct comparison of velocities measured
from Halpha rotation curves in nearby galaxies and from [OII] line widths at
higher redshifts. To provide calibration for the geometrical tests, we give
expressions for the different scaling relations between properties of galaxies
(size, surface brightness, magnitude) and their rotation speeds. Apart from the
Tully-Fisher relation, we derive the size-rotation velocity and surface
brightness-rotation velocity relations with unprecedentedly small scatters. We
show how the best size-rotation velocity relation is derived when size is
estimated not from disc scale lengths but from the isophotal diameter r23.5,
once these have been corrected for inclination and extinction effects.Comment: 14 pages and 10 figures. A&A submitte
Dynamic causal modelling of electrographic seizure activity using Bayesian belief updating
AbstractSeizure activity in EEG recordings can persist for hours with seizure dynamics changing rapidly over time and space. To characterise the spatiotemporal evolution of seizure activity, large data sets often need to be analysed. Dynamic causal modelling (DCM) can be used to estimate the synaptic drivers of cortical dynamics during a seizure; however, the requisite (Bayesian) inversion procedure is computationally expensive. In this note, we describe a straightforward procedure, within the DCM framework, that provides efficient inversion of seizure activity measured with non-invasive and invasive physiological recordings; namely, EEG/ECoG. We describe the theoretical background behind a Bayesian belief updating scheme for DCM. The scheme is tested on simulated and empirical seizure activity (recorded both invasively and non-invasively) and compared with standard Bayesian inversion. We show that the Bayesian belief updating scheme provides similar estimates of time-varying synaptic parameters, compared to standard schemes, indicating no significant qualitative change in accuracy. The difference in variance explained was small (less than 5%). The updating method was substantially more efficient, taking approximately 5–10min compared to approximately 1–2h. Moreover, the setup of the model under the updating scheme allows for a clear specification of how neuronal variables fluctuate over separable timescales. This method now allows us to investigate the effect of fast (neuronal) activity on slow fluctuations in (synaptic) parameters, paving a way forward to understand how seizure activity is generated
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