405,826 research outputs found
Separable time-causal and time-recursive spatio-temporal receptive fields
We present an improved model and theory for time-causal and time-recursive
spatio-temporal receptive fields, obtained by a combination of Gaussian
receptive fields over the spatial domain and first-order integrators or
equivalently truncated exponential filters coupled in cascade over the temporal
domain. Compared to previous spatio-temporal scale-space formulations in terms
of non-enhancement of local extrema or scale invariance, these receptive fields
are based on different scale-space axiomatics over time by ensuring
non-creation of new local extrema or zero-crossings with increasing temporal
scale. Specifically, extensions are presented about parameterizing the
intermediate temporal scale levels, analysing the resulting temporal dynamics
and transferring the theory to a discrete implementation in terms of recursive
filters over time.Comment: 12 pages, 2 figures, 2 tables. arXiv admin note: substantial text
overlap with arXiv:1404.203
Model of a fluid at small and large length scales and the hydrophobic effect
We present a statistical field theory to describe large length scale effects
induced by solutes in a cold and otherwise placid liquid. The theory divides
space into a cubic grid of cells. The side length of each cell is of the order
of the bulk correlation length of the bulk liquid. Large length scale states of
the cells are specified with an Ising variable. Finer length scale effects are
described with a Gaussian field, with mean and variance affected by both the
large length scale field and by the constraints imposed by solutes. In the
absence of solutes and corresponding constraints, integration over the Gaussian
field yields an effective lattice gas Hamiltonian for the large length scale
field. In the presence of solutes, the integration adds additional terms to
this Hamiltonian. We identify these terms analytically. They can provoke large
length scale effects, such as the formation of interfaces and depletion layers.
We apply our theory to compute the reversible work to form a bubble in liquid
water, as a function of the bubble radius. Comparison with molecular simulation
results for the same function indicates that the theory is reasonably accurate.
Importantly, simulating the large length scale field involves binary arithmetic
only. It thus provides a computationally convenient scheme to incorporate
explicit solvent dynamics and structure in simulation studies of large
molecular assemblies
Increasing the Fisher Information Content in the Matter Power Spectrum by Non-linear Wavelet Weiner Filtering
We develop a purely mathematical tool to recover some of the information lost
in the non-linear collapse of large-scale structure. From a set of 141
simulations of dark matter density fields, we construct a non-linear Weiner
filter in order to separate Gaussian and non-Gaussian structure in wavelet
space. We find that the non-Gaussian power is dominant at smaller scales, as
expected from the theory of structure formation, while the Gaussian counterpart
is damped by an order of magnitude on small scales. We find that it is possible
to increase the Fisher information by a factor of three before reaching the
translinear plateau, an effect comparable to other techniques like the linear
reconstruction of the density field.Comment: 7 pages, 6 figures. Accepted for publication in The Astrophysical
Journa
Non-Gaussianity vs. non-linearity of cosmological perturbations
Following the discovery of the CMB, the hot big-bang model has become the
standard cosmological model. In this theory, small primordial fluctuations are
subsequently amplified by gravity to form the large-scale structure seen today.
Different theories for unified models of particle physics, lead to different
predictions for the statistical properties of the primordial fluctuations, that
can be divided in two classes: gaussian and non-gaussian. Convincing evidence
against or for gaussian initial conditions would rule out many scenarios and
point us towards a physical theory for the origin of structures. The
statistical distribution of cosmological perturbations, as we observe them, can
deviate from the gaussian distribution in several different ways. Even if
perturbations start off gaussian, non-linear gravitational evolution can
introduce non-gaussian features. Additionally, our knowledge of the Universe
comes principally from the study of luminous material such as galaxies, but
these might not be faithful tracers of the underlying mass distribution. The
relationship between fluctuations in the mass and in the galaxies distribution
(bias), is often assumed to be local, but could well be non-linear. Moreover,
galaxy catalogues use the redshift as third spatial coordinate: the resulting
redshift-space map is non-linearly distorted by peculiar velocities. Non-linear
gravitational evolution, biasing, and redshift-space distortion introduce
non-gaussianity, even in an initially gaussian fluctuation field. I will
investigate the statistical tools that allow us, in principle, to disentangle
the above different effects, and the observational datasets we require to do so
in practice.Comment: To appear in proc. of the 15th Florida workshop in Nonlinear
Astronomy and Physics. Annals of The New York Academy of Science
Time-causal and time-recursive spatio-temporal receptive fields
We present an improved model and theory for time-causal and time-recursive
spatio-temporal receptive fields, based on a combination of Gaussian receptive
fields over the spatial domain and first-order integrators or equivalently
truncated exponential filters coupled in cascade over the temporal domain.
Compared to previous spatio-temporal scale-space formulations in terms of
non-enhancement of local extrema or scale invariance, these receptive fields
are based on different scale-space axiomatics over time by ensuring
non-creation of new local extrema or zero-crossings with increasing temporal
scale. Specifically, extensions are presented about (i) parameterizing the
intermediate temporal scale levels, (ii) analysing the resulting temporal
dynamics, (iii) transferring the theory to a discrete implementation, (iv)
computing scale-normalized spatio-temporal derivative expressions for
spatio-temporal feature detection and (v) computational modelling of receptive
fields in the lateral geniculate nucleus (LGN) and the primary visual cortex
(V1) in biological vision.
We show that by distributing the intermediate temporal scale levels according
to a logarithmic distribution, we obtain much faster temporal response
properties (shorter temporal delays) compared to a uniform distribution.
Specifically, these kernels converge very rapidly to a limit kernel possessing
true self-similar scale-invariant properties over temporal scales, thereby
allowing for true scale invariance over variations in the temporal scale,
although the underlying temporal scale-space representation is based on a
discretized temporal scale parameter.
We show how scale-normalized temporal derivatives can be defined for these
time-causal scale-space kernels and how the composed theory can be used for
computing basic types of scale-normalized spatio-temporal derivative
expressions in a computationally efficient manner.Comment: 39 pages, 12 figures, 5 tables in Journal of Mathematical Imaging and
Vision, published online Dec 201
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