129,373 research outputs found
Local-To-Global Agreement Expansion via the Variance Method
Agreement expansion is concerned with set systems for which local assignments to the sets with almost perfect pairwise consistency (i.e., most overlapping pairs of sets agree on their intersections) implies the existence of a global assignment to the ground set (from which the sets are defined) that agrees with most of the local assignments.
It is currently known that if a set system forms a two-sided or a partite high dimensional expander then agreement expansion is implied. However, it was not known whether agreement expansion can be implied for one-sided high dimensional expanders.
In this work we show that agreement expansion can be deduced for one-sided high dimensional expanders assuming that all the vertices\u27 links (i.e., the neighborhoods of the vertices) are agreement expanders. Thus, for one-sided high dimensional expander, an agreement expansion of the large complicated complex can be deduced from agreement expansion of its small simple links.
Using our result, we settle the open question whether the well studied Ramanujan complexes are agreement expanders. These complexes are neither partite nor two-sided high dimensional expanders. However, they are one-sided high dimensional expanders for which their links are partite and hence are agreement expanders. Thus, our result implies that Ramanujan complexes are agreement expanders, answering affirmatively the aforementioned open question.
The local-to-global agreement expansion that we prove is based on the variance method that we develop. We show that for a high dimensional expander, if we define a function on its top faces and consider its local averages over the links then the variance of these local averages is much smaller than the global variance of the original function. This decreasing in the variance enables us to construct one global agreement function that ties together all local agreement functions
Testing for a large local void by investigating the Near-Infrared Galaxy Luminosity Function
Recent cosmological modeling efforts have shown that a local underdensity on
scales of a few hundred Mpc (out to z ~ 0.1), could produce the apparent
acceleration of the expansion of the universe observed via type Ia supernovae.
Several studies of galaxy counts in the near-infrared (NIR) have found that the
local universe appears under-dense by ~25-50% compared with regions a few
hundred Mpc distant. Galaxy counts at low redshifts sample primarily L ~ L*
galaxies. Thus, if the local universe is under-dense, then the normalization of
the NIR galaxy luminosity function (LF) at z>0.1 should be higher than that
measured for z 90%) spectroscopic
sample of 1436 galaxies selected in the H-band to study the normalization of
the NIR LF at 0.1<z<0.3 and address the question of whether or not we reside in
a large local underdensity. We find that for the combination of our six fields,
the product phi* L* at 0.1 < z < 0.3 is ~ 30% higher than that measured at
lower redshifts. While our statistical errors in this measurement are on the
~10% level, we find the systematics due to cosmic variance may be larger still.
We investigate the effects of cosmic variance on our measurement using the
COSMOS cone mock catalogs from the Millennium simulation and recent empirical
estimates. We find that our survey is subject to systematic uncertainties due
to cosmic variance at the 15% level ($1 sigma), representing an improvement by
a factor of ~ 2 over previous studies in this redshift range. We conclude that
observations cannot yet rule out the possibility that the local universe is
under-dense at z<0.1.Comment: Accepted for publication in Ap
Fitting Effective Diffusion Models to Data Associated with a "Glassy Potential": Estimation, Classical Inference Procedures and Some Heuristics
A variety of researchers have successfully obtained the parameters of low
dimensional diffusion models using the data that comes out of atomistic
simulations. This naturally raises a variety of questions about efficient
estimation, goodness-of-fit tests, and confidence interval estimation. The
first part of this article uses maximum likelihood estimation to obtain the
parameters of a diffusion model from a scalar time series. I address numerical
issues associated with attempting to realize asymptotic statistics results with
moderate sample sizes in the presence of exact and approximated transition
densities. Approximate transition densities are used because the analytic
solution of a transition density associated with a parametric diffusion model
is often unknown.I am primarily interested in how well the deterministic
transition density expansions of Ait-Sahalia capture the curvature of the
transition density in (idealized) situations that occur when one carries out
simulations in the presence of a "glassy" interaction potential. Accurate
approximation of the curvature of the transition density is desirable because
it can be used to quantify the goodness-of-fit of the model and to calculate
asymptotic confidence intervals of the estimated parameters. The second part of
this paper contributes a heuristic estimation technique for approximating a
nonlinear diffusion model. A "global" nonlinear model is obtained by taking a
batch of time series and applying simple local models to portions of the data.
I demonstrate the technique on a diffusion model with a known transition
density and on data generated by the Stochastic Simulation Algorithm.Comment: 30 pages 10 figures Submitted to SIAM MMS (typos removed and slightly
shortened
Flow Fluctuations from Early-Time Correlations in Nuclear Collisions
We propose that flow fluctuations have the same origin as transverse momentum
fluctuations. The common source of these fluctuations is the spatially
inhomogeneous initial state that drives hydrodynamic flow. Longitudinal
correlations from an early Glasma stage followed by hydrodynamic flow
quantitatively account for many features of multiplicity and fluctuation
data. We develop a framework for studying flow and its fluctuations in this
picture. We then compute elliptic and triangular flow fluctuations, and study
their connections to the ridge
Spatial variation of total column ozone on a global scale
The spatial dependence of total column ozone varies strongly with latitude,
so that homogeneous models (invariant to all rotations) are clearly unsuitable.
However, an assumption of axial symmetry, which means that the process model is
invariant to rotations about the Earth's axis, is much more plausible and
considerably simplifies the modeling. Using TOMS (Total Ozone Mapping
Spectrometer) measurements of total column ozone over a six-day period, this
work investigates the modeling of axially symmetric processes on the sphere
using expansions in spherical harmonics. It turns out that one can capture many
of the large scale features of the spatial covariance structure using a
relatively small number of terms in such an expansion, but the resulting fitted
model provides a horrible fit to the data when evaluated via its likelihood
because of its inability to describe accurately the process's local behavior.
Thus, there remains the challenge of developing computationally tractable
models that capture both the large and small scale structure of these data.Comment: Published at http://dx.doi.org/10.1214/07-AOAS106 in the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Fluctuations of quantum fields via zeta function regularization
Explicit expressions for the expectation values and the variances of some
observables, which are bilinear quantities in the quantum fields on a
D-dimensional manifold, are derived making use of zeta function regularization.
It is found that the variance, related to the second functional variation of
the effective action, requires a further regularization and that the relative
regularized variance turns out to be 2/N, where N is the number of the fields,
thus being independent on the dimension D. Some illustrating examples are
worked through.Comment: 15 pages, latex, typographical mistakes correcte
The stability of the O(N) invariant fixed point in three dimensions
We study the stability of the O(N) fixed point in three dimensions under
perturbations of the cubic type. We address this problem in the three cases
by using finite size scaling techniques and high precision Monte
Carlo simulations. It is well know that there is a critical value
below which the O(N) fixed point is stable and above which the cubic fixed
point becomes the stable one. While we cannot exclude that , as recently
claimed by Kleinert and collaborators, our analysis strongly suggests that
coincides with 3.Comment: latex file of 18 pages plus three ps figure
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