1,008 research outputs found
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
Idealized computational models for auditory receptive fields
This paper presents a theory by which idealized models of auditory receptive
fields can be derived in a principled axiomatic manner, from a set of
structural properties to enable invariance of receptive field responses under
natural sound transformations and ensure internal consistency between
spectro-temporal receptive fields at different temporal and spectral scales.
For defining a time-frequency transformation of a purely temporal sound
signal, it is shown that the framework allows for a new way of deriving the
Gabor and Gammatone filters as well as a novel family of generalized Gammatone
filters, with additional degrees of freedom to obtain different trade-offs
between the spectral selectivity and the temporal delay of time-causal temporal
window functions.
When applied to the definition of a second-layer of receptive fields from a
spectrogram, it is shown that the framework leads to two canonical families of
spectro-temporal receptive fields, in terms of spectro-temporal derivatives of
either spectro-temporal Gaussian kernels for non-causal time or the combination
of a time-causal generalized Gammatone filter over the temporal domain and a
Gaussian filter over the logspectral domain. For each filter family, the
spectro-temporal receptive fields can be either separable over the
time-frequency domain or be adapted to local glissando transformations that
represent variations in logarithmic frequencies over time. Within each domain
of either non-causal or time-causal time, these receptive field families are
derived by uniqueness from the assumptions.
It is demonstrated how the presented framework allows for computation of
basic auditory features for audio processing and that it leads to predictions
about auditory receptive fields with good qualitative similarity to biological
receptive fields measured in the inferior colliculus (ICC) and primary auditory
cortex (A1) of mammals.Comment: 55 pages, 22 figures, 3 table
Eddy current defect response analysis using sum of Gaussian methods
This dissertation is a study of methods to automatedly detect and produce approximations of eddy current differential coil defect signatures in terms of a summed collection of Gaussian functions (SoG). Datasets consisting of varying material, defect size, inspection frequency, and coil diameter were investigated. Dimensionally reduced representations of the defect responses were obtained utilizing common existing reduction methods and novel enhancements to them utilizing SoG Representations. Efficacy of the SoG enhanced representations were studied utilizing common Machine Learning (ML) interpretable classifier designs with the SoG representations indicating significant improvement of common analysis metrics
Continuation for thin film hydrodynamics and related scalar problems
This chapter illustrates how to apply continuation techniques in the analysis
of a particular class of nonlinear kinetic equations that describe the time
evolution through transport equations for a single scalar field like a
densities or interface profiles of various types. We first systematically
introduce these equations as gradient dynamics combining mass-conserving and
nonmass-conserving fluxes followed by a discussion of nonvariational amendmends
and a brief introduction to their analysis by numerical continuation. The
approach is first applied to a number of common examples of variational
equations, namely, Allen-Cahn- and Cahn-Hilliard-type equations including
certain thin-film equations for partially wetting liquids on homogeneous and
heterogeneous substrates as well as Swift-Hohenberg and Phase-Field-Crystal
equations. Second we consider nonvariational examples as the
Kuramoto-Sivashinsky equation, convective Allen-Cahn and Cahn-Hilliard
equations and thin-film equations describing stationary sliding drops and a
transversal front instability in a dip-coating. Through the different examples
we illustrate how to employ the numerical tools provided by the packages
auto07p and pde2path to determine steady, stationary and time-periodic
solutions in one and two dimensions and the resulting bifurcation diagrams. The
incorporation of boundary conditions and integral side conditions is also
discussed as well as problem-specific implementation issues
Optimization of Trading Physics Models of Markets
We describe an end-to-end real-time S&P futures trading system. Inner-shell
stochastic nonlinear dynamic models are developed, and Canonical Momenta
Indicators (CMI) are derived from a fitted Lagrangian used by outer-shell
trading models dependent on these indicators. Recursive and adaptive
optimization using Adaptive Simulated Annealing (ASA) is used for fitting
parameters shared across these shells of dynamic and trading models
Pseudospectral discretization of nonlinear delay equations: new prospects for numerical bifurcation analysis
We apply the pseudospectral discretization approach to nonlinear delay models described by delay differential equations, renewal equations or systems of coupled renewal equations and delay differential equations. The aim is to derive ordinary differential equations and to investigate the stability and bifurcation of equilibria of the original model by available software packages for continuation and bifurcation for ordinary differential equations. Theoretical and numerical results confirm the effectiveness and the versatility of the approach, opening a new perspective for the bifurcation analysis of delay equations, in particular coupled renewal and delay differential equations
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