122,696 research outputs found
Improved Compressive Sensing Of Natural Scenes Using Localized Random Sampling
Compressive sensing (CS) theory demonstrates that by using uniformly-random sampling, rather than uniformly-spaced sampling, higher quality image reconstructions are often achievable. Considering that the structure of sampling protocols has such a profound impact on the quality of image reconstructions, we formulate a new sampling scheme motivated by physiological receptive field structure, localized random sampling, which yields significantly improved CS image reconstructions. For each set of localized image measurements, our sampling method first randomly selects an image pixel and then measures its nearby pixels with probability depending on their distance from the initially selected pixel. We compare the uniformly-random and localized random sampling methods over a large space of sampling parameters, and show that, for the optimal parameter choices, higher quality image reconstructions can be consistently obtained by using localized random sampling. In addition, we argue that the localized random CS optimal parameter choice is stable with respect to diverse natural images, and scales with the number of samples used for reconstruction. We expect that the localized random sampling protocol helps to explain the evolutionarily advantageous nature of receptive field structure in visual systems and suggests several future research areas in CS theory and its application to brain imaging
Efficient Image Processing Via Compressive Sensing Of Integrate-And-Fire Neuronal Network Dynamics
Integrate-and-fire (I&F) neuronal networks are ubiquitous in diverse image processing applications, including image segmentation and visual perception. While conventional I&F network image processing requires the number of nodes composing the network to be equal to the number of image pixels driving the network, we determine whether I&F dynamics can accurately transmit image information when there are significantly fewer nodes than network input-signal components. Although compressive sensing (CS) theory facilitates the recovery of images using very few samples through linear signal processing, it does not address whether similar signal recovery techniques facilitate reconstructions through measurement of the nonlinear dynamics of an I&F network. In this paper, we present a new framework for recovering sparse inputs of nonlinear neuronal networks via compressive sensing. By recovering both one-dimensional inputs and two-dimensional images, resembling natural stimuli, we demonstrate that input information can be well-preserved through nonlinear I&F network dynamics even when the number of network-output measurements is significantly smaller than the number of input-signal components. This work suggests an important extension of CS theory potentially useful in improving the processing of medical or natural images through I&F network dynamics and understanding the transmission of stimulus information across the visual system
Pulling hairpinned polynucleotide chains: Does base-pair stacking interaction matter?
Force-induced structural transitions both in relatively random and in
designed single-stranded DNA (ssDNA) chains are studied theoretically. At high
salt conditions, ssDNA forms compacted hairpin patterns stabilized by
base-pairing and base-pair stacking interactions, and a threshold external
force is needed to pull the hairpinned structure into a random coiled one. The
base-pair stacking interaction in the ssDNA chain makes this hairpin-coil
conversion a discontinuous (first-order) phase transition process characterized
by a force plateau in the force-extension curve, while lowering this potential
below some critical level turns this transition into continuous (second-order)
type, no matter how strong the base-pairing interaction is. The phase diagram
(including hairpin-I, -II, and random coil) is discussed as a function of
stacking potential and external force. These results are in quantitative
agreement with recent experimental observations of different ssDNA sequences,
and they reveal the necessity to consider the base-pair stacking interactions
in order to understand the structural formation of RNA, a polymer designed by
nature itself. The theoretical method used may be extended to study the
long-range interaction along double-stranded DNA caused by the topological
constraint of fixed linking number.Comment: 8 pages using Revte
Quantum computation with un-tunable couplings
Most quantum computer realizations require the ability to apply local fields
and tune the couplings between qubits, in order to realize single bit and two
bit gates which are necessary for universal quantum computation. We present a
scheme to remove the necessity of switching the couplings between qubits for
two bit gates, which are more costly in many cases. Our strategy is to compute
in and out of carefully designed interaction free subspaces analogous to
decoherence free subspaces, which allows us to effectively turn off and turn on
the interactions between the encoded qubits. We give two examples to show how
universal quantum computation is realized in our scheme with local
manipulations to physical qubits only, for both diagonal and off diagonal
interactions.Comment: 5 pages, 2 figure
Gravity Waves as a Probe of Hubble Expansion Rate During An Electroweak Scale Phase Transition
Just as big bang nucleosynthesis allows us to probe the expansion rate when
the temperature of the universe was around 1 MeV, the measurement of gravity
waves from electroweak scale first order phase transitions may allow us to
probe the expansion rate when the temperature of the universe was at the
electroweak scale. We compute the simple transformation rule for the gravity
wave spectrum under the scaling transformation of the Hubble expansion rate. We
then apply this directly to the scenario of quintessence kination domination
and show how gravity wave spectra would shift relative to LISA and BBO
projected sensitivities.Comment: 28 pages, 2 figures
Significance of interface anisotropy in laser induced magnetization precession in ferromagnetic metal films
Laser induced ultrafast demagnetization in ferromagnetic metals was
discovered almost 20 years ago, but currently there is still lack of consensus
on the microscopic mechanism responsible for the corresponding transfer of
angular momentum and energy between electron, lattice and spin subsystems. A
distinct, but intrinsically correlated phenomenon occurring on a longer
timescale is the magnetization precession after the ultrafast demagnetization
process, if a magnetic field is applied to tilt the magnetization vector away
from its easy direction, which can be attributed to the change of anisotropy
after laser heating. In an in-plane magnetized Pt/Co/Pt thin film with
perpendicular interface anisotropy, we found excellent agreement between
theoretical prediction with plausible parameters and experimental data measured
using time resolved magneto-optical Kerr effect. This agreement confirms that
the time evolution of the anisotropy field, which is driven by the interaction
between electrons and phonons, determines the magnetization precession
completely. A detailed analysis shows that, even though the whole sample is
magnetized in-plane, the dynamic interface anisotropy field dictates the
initial phase of the magnetization precession, highlighting the significance of
the interface anisotropy field in laser induced magnetization precession.Comment: 11 pages, 2 figure
The Gentlest Ascent Dynamics
Dynamical systems that describe the escape from the basins of attraction of
stable invariant sets are presented and analyzed. It is shown that the stable
fixed points of such dynamical systems are the index-1 saddle points.
Generalizations to high index saddle points are discussed. Both gradient and
non-gradient systems are considered. Preliminary results on the nature of the
dynamical behavior are presented
- …