7,550 research outputs found
Relaxation oscillations in a class of delay-differential equations.
We study a class of delay differential equations which have been used to model hematological stem cell regulation and dynamics. Under certain circumstances the model exhibits self-sustained oscillations, with periods which can be significantly longer than the basic cell cycle time. We show that the long periods in the oscillations occur when the cell generation rate is small, and we provide an asymptotic analysis of the model in this case. This analysis bears a close resemblance to the analysis of relaxation oscillators (such as the Van der Pol oscillator), except that in our case the slow manifold is infinite dimensional. Despite this, a fairly complete analysis of the problem is possible
A double main sequence turn-off in the rich star cluster NGC 1846 in the Large Magellanic Cloud
We report on HST/ACS photometry of the rich intermediate-age star cluster NGC
1846 in the Large Magellanic Cloud, which clearly reveals the presence of a
double main sequence turn-off in this object. Despite this, the main sequence,
sub-giant branch, and red giant branch are all narrow and well-defined, and the
red clump is compact. We examine the spatial distribution of turn-off stars and
demonstrate that all belong to NGC 1846 rather than to any field star
population. In addition, the spatial distributions of the two sets of turn-off
stars may exhibit different central concentrations and some asymmetries. By
fitting isochrones, we show that the properties of the colour-magnitude diagram
can be explained if there are two stellar populations of equivalent metal
abundance in NGC 1846, differing in age by approximately 300 Myr. The absolute
ages of the two populations are ~1.9 and ~2.2 Gyr, although there may be a
systematic error of up to +/-0.4 Gyr in these values. The metal abundance
inferred from isochrone fitting is [M/H] ~ -0.40, consistent with spectroscopic
measurements of [Fe/H]. We propose that the observed properties of NGC 1846 can
be explained if this object originated via the tidal capture of two star
clusters formed separately in a star cluster group in a single giant molecular
cloud. This scenario accounts naturally for the age difference and uniform
metallicity of the two member populations, as well as the differences in their
spatial distributions.Comment: 9 pages, 8 figures, accepted for publication in MNRAS. A version with
full resolution figures may be obtained at
http://www.roe.ac.uk/~dmy/papers/MN-07-0441-MJ_rv.ps.gz (postscript) or at
http://www.roe.ac.uk/~dmy/papers/MN-07-0441-MJ_rv.pdf (PDF
Deriving Matrix Concentration Inequalities from Kernel Couplings
This paper derives exponential tail bounds and polynomial moment inequalities
for the spectral norm deviation of a random matrix from its mean value. The
argument depends on a matrix extension of Stein's method of exchangeable pairs
for concentration of measure, as introduced by Chatterjee. Recent work of
Mackey et al. uses these techniques to analyze random matrices with additive
structure, while the enhancements in this paper cover a wider class of
matrix-valued random elements. In particular, these ideas lead to a bounded
differences inequality that applies to random matrices constructed from weakly
dependent random variables. The proofs require novel trace inequalities that
may be of independent interest.Comment: 29 page
Quantization on a torus without position operators
We formulate quantum mechanics in the two-dimensional torus without using
position operators. We define an algebra with only momentum operators and shift
operators and construct irreducible representation of the algebra. We show that
it realizes quantum mechanics of a charged particle in a uniform magnetic
field. We prove that any irreducible representation of the algebra is unitary
equivalent to each other. This work provides a firm foundation for the
noncommutative torus theory.Comment: 12 pages, LaTeX2e, the title is changed, minor corrections are made,
references are added. To be published in Modern Physics Letters
Driver Success in the NASCAR Sprint Cup Series: The Impact of Multi-Car Teams
This paper explores the impact of multi-car teams on driver wins, total points, and total earnings in the NASCAR Sprint Cup Series for the years of 2005 through 2008. Early in NASCAR’s history, multi-car teams were rare as the conventional wisdom was that multi-car teams would have poor chemistry which would negatively impact driver performance. Recently, however, multi-car teams have become more popular. Using season-level data, we show that multi-car teams generally enjoy a competitive advantage on the track over single-car teams but that diminishing returns to the number of cars on a team mitigates the motivation for arbitrarily large teams.peer effects, returns to scale, motor sports
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