13,454 research outputs found
A statistical approach to persistent homology
Assume that a finite set of points is randomly sampled from a subspace of a
metric space. Recent advances in computational topology have provided several
approaches to recovering the geometric and topological properties of the
underlying space. In this paper we take a statistical approach to this problem.
We assume that the data is randomly sampled from an unknown probability
distribution. We define two filtered complexes with which we can calculate the
persistent homology of a probability distribution. Using statistical estimators
for samples from certain families of distributions, we show that we can recover
the persistent homology of the underlying distribution.Comment: 30 pages, 2 figures, minor changes, to appear in Homology, Homotopy
and Application
Eccentricity Evolution for Planets in Gaseous Disks
We investigate the hypothesis that interactions between a giant planet and
the disk from which it forms promote eccentricity growth. These interactions
are concentrated at discrete Lindblad and corotation resonances. Interactions
at principal Lindblad resonances cause the planet's orbit to migrate and open a
gap in the disk if the planet is sufficiently massive. Those at first order
Lindblad and corotation resonances change the planet's orbital eccentricity.
Eccentricity is excited by interactions at external Lindblad resonances which
are located on the opposite side of corotation from the planet, and damped by
co-orbital Lindblad resonances which overlap the planet's orbit. If the planet
clears a gap in the disk, the rate of eccentricity damping by co-orbital
Lindblad resonances is reduced. Density gradients associated with the gap
activate eccentricity damping by corotation resonances at a rate which
initially marginally exceeds that of eccentricity excitation by external
Lindblad resonances. But the corotation torque drives a mass flux which reduces
the density gradient near the resonance. Sufficient partial saturation of
corotation resonances can tip the balance in favor of eccentricity excitation.
A minimal initial eccentricity of a few percent is required to overcome viscous
diffusion which acts to unsaturate corotation resonances by reestablishing the
large scale density gradient. Thus eccentricity growth is a finite amplitude
instability. Formally, interactions at the apsidal resonance, which is a
special kind of co-orbital Lindblad resonance, appears to damp eccentricity
faster than external Lindblad resonances can excite it. However, apsidal waves
have such long wavelengths that they do not propagate in protoplanetary disks.
This reduces eccentricity damping by the apsidal resonance to a modest level.Comment: Submitted to Ap
THE EFFECTS OF HOUSING PRICES, WAGES, AND COMMUTING TIME ON JOINT RESIDENTIAL AND JOB LOCATION CHOICES
A utility maximizing framework is used to model how wages, housing prices, and commuting time affect joint decisions of where to live and where to work. The implied multinomial logit model yields plausible estimates of the role of economic variables on joint residence/job location choices.Labor and Human Capital,
Label-free optical detection of single enzyme-reactant reactions and associated conformational changes
Monitoring the kinetics and conformational dynamics of single enzymes is
crucial in order to better understand their biological functions as these
motions and structural dynamics are usually unsynchronized among the molecules.
Detecting the enzyme-reactant interactions and associated conformational
changes of the enzyme on a single molecule basis, however, remain as a
challenge with established optical techniques due to the commonly required
labeling of the reactants or the enzyme itself. The labeling process is usually
non-trivial and the labels themselves might skew the physical properties of the
enzyme. Here we demonstrate an optical, label-free method capable of observing
enzymatic interactions and the associated conformational changes on the single
molecule level. We monitor polymerase/DNA interactions via the strong
near-field enhancement provided by plasmonic nanorods resonantly coupled to
whispering gallery modes in microcavities. Specifically, we employ two
different recognition schemes: one in which the kinetics of polymerase/DNA
interactions are probed in the vicinity of DNA-functionalized nanorods, and the
other in which these interactions are probed via the magnitude of
conformational changes in the polymerase molecules immobilized on nanorods. In
both approaches we find that low and high polymerase activities can be clearly
discerned via their characteristic signal amplitude and signal length
distributions. Furthermore, the thermodynamic study of the monitored
interactions suggests the occurrence of DNA polymerization. This work
constitutes a proof-of-concept study of enzymatic activities via plasmonically
enhanced microcavities and establishes an alternative and label-free method
capable of investigating structural changes in single molecules
Multi-scale Optics for Enhanced Light Collection from a Point Source
High efficiency collection of photons emitted by a point source over a wide
field-of-view (FoV) is crucial for many applications. Multi-scale optics over
improved light collection by utilizing small optical components placed close to
the optical source, while maintaining a wide FoV provided by conventional
imaging optics. In this work, we demonstrate collection efficiency of 26% of
photons emitted by a point-like source using a micromirror fabricated in
silicon with no significant decrease in collection efficiency over a 10 mm
object space.Comment: 4 pages, 4 figure
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