20,955 research outputs found
The intrinsic value of HFO features as a biomarker of epileptic activity
High frequency oscillations (HFOs) are a promising biomarker of epileptic
brain tissue and activity. HFOs additionally serve as a prototypical example of
challenges in the analysis of discrete events in high-temporal resolution,
intracranial EEG data. Two primary challenges are 1) dimensionality reduction,
and 2) assessing feasibility of classification. Dimensionality reduction
assumes that the data lie on a manifold with dimension less than that of the
feature space. However, previous HFO analyses have assumed a linear manifold,
global across time, space (i.e. recording electrode/channel), and individual
patients. Instead, we assess both a) whether linear methods are appropriate and
b) the consistency of the manifold across time, space, and patients. We also
estimate bounds on the Bayes classification error to quantify the distinction
between two classes of HFOs (those occurring during seizures and those
occurring due to other processes). This analysis provides the foundation for
future clinical use of HFO features and buides the analysis for other discrete
events, such as individual action potentials or multi-unit activity.Comment: 5 pages, 5 figure
Extrinsic Methods for Coding and Dictionary Learning on Grassmann Manifolds
Sparsity-based representations have recently led to notable results in
various visual recognition tasks. In a separate line of research, Riemannian
manifolds have been shown useful for dealing with features and models that do
not lie in Euclidean spaces. With the aim of building a bridge between the two
realms, we address the problem of sparse coding and dictionary learning over
the space of linear subspaces, which form Riemannian structures known as
Grassmann manifolds. To this end, we propose to embed Grassmann manifolds into
the space of symmetric matrices by an isometric mapping. This in turn enables
us to extend two sparse coding schemes to Grassmann manifolds. Furthermore, we
propose closed-form solutions for learning a Grassmann dictionary, atom by
atom. Lastly, to handle non-linearity in data, we extend the proposed Grassmann
sparse coding and dictionary learning algorithms through embedding into Hilbert
spaces.
Experiments on several classification tasks (gender recognition, gesture
classification, scene analysis, face recognition, action recognition and
dynamic texture classification) show that the proposed approaches achieve
considerable improvements in discrimination accuracy, in comparison to
state-of-the-art methods such as kernelized Affine Hull Method and
graph-embedding Grassmann discriminant analysis.Comment: Appearing in International Journal of Computer Visio
Universal features and tail analysis of the order-parameter distribution of the two-dimensional Ising model: An entropic sampling Monte Carlo study
We present a numerical study of the order-parameter probability density
function (PDF) of the square Ising model for lattices with linear sizes
. A recent efficient entropic sampling scheme, combining the
Wang-Landau and broad histogram methods and based on the high-levels of the
Wang-Landau process in dominant energy subspaces is employed. We find that for
large lattices there exists a stable window of the scaled order-parameter in
which the full ansatz including the pre-exponential factor for the tail regime
of the universal PDF is well obeyed. This window is used to estimate the
equation of state exponent and to observe the behavior of the universal
constants implicit in the functional form of the universal PDF. The probability
densities are used to estimate the universal Privman-Fisher coefficient and to
investigate whether one could obtain reliable estimates of the universal
constants controlling the asymptotic behavior of the tail regime.Comment: 24 pages, 5 figure
The Weak Coupling Spectrum around Isolated Vacua in N=4 Super Yang-Mills on T^3 with any Gauge Group
The moduli space of flat connections for maximally supersymmetric Yang-Mills
theories, in a space-time of the form T^3xR, contains isolated points,
corresponding to normalizable zero energy states, for certain simple gauge
groups G. We consider the low energy effective field theories in the weak
coupling limit supported on such isolated points and find that when quantized
they consist of an infinite set of harmonic oscillators whose angular
frequencies are completely determined by the Lie algebra of G. We then proceed
to find the isolated flat connections for all simple G and subsequently specify
the corresponding effective field theories.Comment: 32 pages, 11 figures, v4 Added chapter, Published versio
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