341 research outputs found
Nonlinear model order reduction via Dynamic Mode Decomposition
We propose a new technique for obtaining reduced order models for nonlinear
dynamical systems. Specifically, we advocate the use of the recently developed
Dynamic Mode Decomposition (DMD), an equation-free method, to approximate the
nonlinear term. DMD is a spatio-temporal matrix decomposition of a data matrix
that correlates spatial features while simultaneously associating the activity
with periodic temporal behavior. With this decomposition, one can obtain a
fully reduced dimensional surrogate model and avoid the evaluation of the
nonlinear term in the online stage. This allows for an impressive speed up of
the computational cost, and, at the same time, accurate approximations of the
problem. We present a suite of numerical tests to illustrate our approach and
to show the effectiveness of the method in comparison to existing approaches
Selecting a Small Set of Optimal Gestures from an Extensive Lexicon
Finding the best set of gestures to use for a given computer recognition
problem is an essential part of optimizing the recognition performance while
being mindful to those who may articulate the gestures. An objective function,
called the ellipsoidal distance ratio metric (EDRM), for determining the best
gestures from a larger lexicon library is presented, along with a numerical
method for incorporating subjective preferences. In particular, we demonstrate
an efficient algorithm that chooses the best gestures from a lexicon of
gestures where typically using a weighting of both subjective and
objective measures.Comment: 27 pages, 7 figure
A reaction-diffusion model of cholinergic retinal waves
Prior to receiving visual stimuli, spontaneous, correlated activity called
retinal waves drives activity-dependent developmental programs. Early-stage
waves mediated by acetylcholine (ACh) manifest as slow, spreading bursts of
action potentials. They are believed to be initiated by the spontaneous firing
of Starburst Amacrine Cells (SACs), whose dense, recurrent connectivity then
propagates this activity laterally. Their extended inter-wave intervals and
shifting wave boundaries are the result of the slow after-hyperpolarization of
the SACs creating an evolving mosaic of recruitable and refractory cells, which
can and cannot participate in waves, respectively. Recent evidence suggests
that cholinergic waves may be modulated by the extracellular concentration of
ACh. Here, we construct a simplified, biophysically consistent,
reaction-diffusion model of cholinergic retinal waves capable of recapitulating
wave dynamics observed in mice retina recordings. The dense, recurrent
connectivity of SACs is modeled through local, excitatory coupling occurring
via the volume release and diffusion of ACh. In contrast with previous,
simulation-based models, we are able to use non-linear wave theory to connect
wave features to underlying physiological parameters, making the model useful
in determining appropriate pharmacological manipulations to experimentally
produce waves of a prescribed spatiotemporal character. The model is used to
determine how ACh mediated connectivity may modulate wave activity, and how the
noise rate and sAHP refractory period contributes to critical wave size
variability.Comment: 38 pages, 10 figure
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