147,624 research outputs found
Point stabilisers for the enhanced and exotic nilpotent cones
We give a semi-direct product decomposition of the point stabilisers for the
enhanced and exotic nilpotent cones. In particular, we arrive at formulas for
the number of points in each orbit over a finite field. This is in accordance
with a recent conjecture of Achar and Henderson.Comment: 25 pages->13 pages, presentation simplified. Title altered. To appear
in Journal of Group Theor
Binomial coefficients, Catalan numbers and Lucas quotients
Let be an odd prime and let be integers with and . In this paper we determine
mod for ; for example,
where is the Jacobi symbol, and is the Lucas
sequence given by , and for
. As an application, we determine modulo for any integer , where denotes the
Catalan number . We also pose some related conjectures.Comment: 24 pages. Correct few typo
Constraints on the Star Formation Efficiency of Galaxies During the Epoch of Reionization
Reionization is thought to have occurred in the redshift range of , which is now being probed by both deep galaxy surveys and CMB observations.
Using halo abundance matching over the redshift range and assuming
smooth, continuous gas accretion, we develop a model for the star formation
efficiency of dark matter halos at that matches the measured
galaxy luminosity functions at these redshifts. We find that peaks
at at halo masses --~M, in
qualitative agreement with its behavior at lower redshifts. We then investigate
the cosmic star formation histories and the corresponding models of
reionization for a range of extrapolations to small halo masses. We use a
variety of observations to further constrain the characteristics of the galaxy
populations, including the escape fraction of UV photons. Our approach provides
an empirically-calibrated, physically-motivated model for the properties of
star-forming galaxies sourcing the epoch of reionization. In the case where
star formation in low-mass halos is maximally efficient, an average escape
fraction can reproduce the optical depth reported by Planck, whereas
inefficient star formation in these halos requires either about twice as many
UV photons to escape, or an escape fraction that increases towards higher
redshifts. Our models also predict how future observations with JWST can
improve our understanding of these galaxy populations.Comment: 19 pages, 12 figures, accepted for publication in MNRAS, minor
modification
Eigen-Based Transceivers for the MIMO Broadcast Channel with Semi-Orthogonal User Selection
This paper studies the sum rate performance of two low complexity
eigenmode-based transmission techniques for the MIMO broadcast channel,
employing greedy semi-orthogonal user selection (SUS). The first approach,
termed ZFDPC-SUS, is based on zero-forcing dirty paper coding; the second
approach, termed ZFBF-SUS, is based on zero-forcing beamforming. We first
employ new analytical methods to prove that as the number of users K grows
large, the ZFDPC-SUS approach can achieve the optimal sum rate scaling of the
MIMO broadcast channel. We also prove that the average sum rates of both
techniques converge to the average sum capacity of the MIMO broadcast channel
for large K. In addition to the asymptotic analysis, we investigate the sum
rates achieved by ZFDPC-SUS and ZFBF-SUS for finite K, and show that ZFDPC-SUS
has significant performance advantages. Our results also provide key insights
into the benefit of multiple receive antennas, and the effect of the SUS
algorithm. In particular, we show that whilst multiple receive antennas only
improves the asymptotic sum rate scaling via the second-order behavior of the
multi-user diversity gain; for finite K, the benefit can be very significant.
We also show the interesting result that the semi-orthogonality constraint
imposed by SUS, whilst facilitating a very low complexity user selection
procedure, asymptotically does not reduce the multi-user diversity gain in
either first (log K) or second-order (loglog K) terms.Comment: 35 pages, 3 figures, to appear in IEEE transactions on signal
processin
One-dimensional Voter Model Interface Revisited
We consider the voter model on Z, starting with all 1's to the left of the
origin and all 0's to the right of the origin. It is known that if the
associated random walk kernel p has zero mean and a finite r-th moment for any
r>3, then the evolution of the boundaries of the interface region between 1's
and 0's converge in distribution to a standard Brownian motion (B_t)_{t>0}
under diffusive scaling of space and time. This convergence fails when p has an
infinite r-th moment for any r<3, due to the loss of tightness caused by a few
isolated 1's appearing deep within the regions of all 0's (and vice versa) at
exceptional times. In this note, we show that as long as p has a finite second
moment, the measure-valued process induced by the rescaled voter model
configuration is tight, and converges weakly to the measure-valued process
1_{x0.Comment: revised versio
Recursive Integral Method with Cayley Transformation
Recently, a non-classical eigenvalue solver, called RIM, was proposed to
compute (all) eigenvalues in a region on the complex plane. Without solving any
eigenvalue problem, it tests if a region contains eigenvalues using an
approximate spectral projection. Regions that contain eigenvalues are
subdivided and tested recursively until eigenvalues are isolated with a
specified precision. This makes RIM an eigensolver distinct from all existing
methods. Furthermore, it requires no a priori spectral information. In this
paper, we propose an improved version of {\bf RIM} for non-Hermitian eigenvalue
problems. Using Cayley transformation and Arnoldi's method, the computation
cost is reduced significantly. Effectiveness and efficiency of the new method
are demonstrated by numerical examples and compared with 'eigs' in Matlab
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UV-Photolithography Fabrication of Poly-Ethylene Glycol Hydrogels Encapsulated with Hepatocytes
The development of biomanufacturing technologies particularly, layered manufacturing has
advanced cell encapsulation processes in an effort to mimic the cellular microenvironment for invitro studies. This paper illustrates an inexpensive UV-photolithographic method for
encapsulation of human hepatocytes in three dimensional structures using poly-ethylene
diacrylate (PEGDA) hydrogels as candidate substrates. In order to further develop this
technology for layered fabrication, we have quantified the long-term effects of the photo-initiator
concentration and UV light exposure on the metabolic rates of encapsulated human hepatocytes
under a 21 day study. The photoinitator toxicity was observed immediately after polymerization
with no significant cytotoxicity on a long term basis. A cellular viability is examined and
reported for the UV photopolymerization process. Cell phenotype maintenance was observed by
measuring the amount of urea produced over a 1 week time period. This photo encapsulation
process may find use in the fabrication of spatially complex 3D scaffolds for tissue engineering
applications, elucidation of the 3D structure-pharmacokinetic response relationship and the
fabrication of complex multi-compartment liver tissue analog devices for drug screening
applications.Mechanical Engineerin
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