60,686 research outputs found
Stimulus-invariant processing and spectrotemporal reverse correlation in primary auditory cortex
The spectrotemporal receptive field (STRF) provides a versatile and
integrated, spectral and temporal, functional characterization of single cells
in primary auditory cortex (AI). In this paper, we explore the origin of, and
relationship between, different ways of measuring and analyzing an STRF. We
demonstrate that STRFs measured using a spectrotemporally diverse array of
broadband stimuli -- such as dynamic ripples, spectrotemporally white noise,
and temporally orthogonal ripple combinations (TORCs) -- are very similar,
confirming earlier findings that the STRF is a robust linear descriptor of the
cell. We also present a new deterministic analysis framework that employs the
Fourier series to describe the spectrotemporal modulations contained in the
stimuli and responses. Additional insights into the STRF measurements,
including the nature and interpretation of measurement errors, is presented
using the Fourier transform, coupled to singular-value decomposition (SVD), and
variability analyses including bootstrap. The results promote the utility of
the STRF as a core functional descriptor of neurons in AI.Comment: 42 pages, 8 Figures; to appear in Journal of Computational
Neuroscienc
Computing Nearly Singular Solutions Using Pseudo-Spectral Methods
In this paper, we investigate the performance of pseudo-spectral methods in
computing nearly singular solutions of fluid dynamics equations. We consider
two different ways of removing the aliasing errors in a pseudo-spectral method.
The first one is the traditional 2/3 dealiasing rule. The second one is a high
(36th) order Fourier smoothing which keeps a significant portion of the Fourier
modes beyond the 2/3 cut-off point in the Fourier spectrum for the 2/3
dealiasing method. Both the 1D Burgers equation and the 3D incompressible Euler
equations are considered. We demonstrate that the pseudo-spectral method with
the high order Fourier smoothing gives a much better performance than the
pseudo-spectral method with the 2/3 dealiasing rule. Moreover, we show that the
high order Fourier smoothing method captures about more effective
Fourier modes in each dimension than the 2/3 dealiasing method. For the 3D
Euler equations, the gain in the effective Fourier codes for the high order
Fourier smoothing method can be as large as 20% over the 2/3 dealiasing method.
Another interesting observation is that the error produced by the high order
Fourier smoothing method is highly localized near the region where the solution
is most singular, while the 2/3 dealiasing method tends to produce oscillations
in the entire domain. The high order Fourier smoothing method is also found be
very stable dynamically. No high frequency instability has been observed.Comment: 26 pages, 23 figure
Low-Rank Matrices on Graphs: Generalized Recovery & Applications
Many real world datasets subsume a linear or non-linear low-rank structure in
a very low-dimensional space. Unfortunately, one often has very little or no
information about the geometry of the space, resulting in a highly
under-determined recovery problem. Under certain circumstances,
state-of-the-art algorithms provide an exact recovery for linear low-rank
structures but at the expense of highly inscalable algorithms which use nuclear
norm. However, the case of non-linear structures remains unresolved. We revisit
the problem of low-rank recovery from a totally different perspective,
involving graphs which encode pairwise similarity between the data samples and
features. Surprisingly, our analysis confirms that it is possible to recover
many approximate linear and non-linear low-rank structures with recovery
guarantees with a set of highly scalable and efficient algorithms. We call such
data matrices as \textit{Low-Rank matrices on graphs} and show that many real
world datasets satisfy this assumption approximately due to underlying
stationarity. Our detailed theoretical and experimental analysis unveils the
power of the simple, yet very novel recovery framework \textit{Fast Robust PCA
on Graphs
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