2,294 research outputs found
Nestedness in mutualistic networks
James et al. (2012) presented simulations that apparently falsify the
analytical result by Bastolla et al. (2009), who showed that nested mutualistic
interactions decrease interspecific competition and increase biodiversity in
model ecosystems. This contradiction, however, mainly stems from the incorrect
application of formulas derived for fully connected networks to empirical,
sparse networks.Comment: 2 pages, 1 figur
CMB Anisotropies at Second Order I
We present the computation of the full system of Boltzmann equations at
second-order describing the evolution of the photon, baryon and cold dark
matter fluids. These equations allow to follow the time evolution of the Cosmic
Microwave Background (CMB) anisotropies at second-order at all angular scales
from the early epoch, when the cosmological perturbations were generated, to
the present through the recombination era. This paper sets the stage for the
computation of the full second-order radiation transfer function at all scales
and for a a generic set of initial conditions specifying the level of
primordial non-Gaussianity. In a companion paper, we will present the
computation of the three-point correlation function at recombination which is
so relevant for the issue of non-Gaussianity in the CMB anisotropies.Comment: 26 pages, LaTeX file, typos correcte
On the non-Gaussianity from Recombination
The non-linear effects operating at the recombination epoch generate a
non-Gaussian signal in the CMB anisotropies. Such a contribution is relevant
because it represents a major part of the second-order radiation transfer
function which must be determined in order to have a complete control of both
the primordial and non-primordial part of non-Gaussianity in the CMB
anisotropies. We provide an estimate of the level of non-Gaussianity in the CMB
arising from the recombination epoch which shows up mainly in the equilateral
configuration. We find that it causes a contamination to the possible
measurement of the equilateral primordial bispectrum shifting the minimum
detectable value of the non-Gaussian parameter f^equil_NL by Delta f^equil_NL=
O(10) for an experiment like Planck.Comment: LaTeX file; 11 pages. v2: Typos corrected; references added; comments
about the effective non-linearity parameter added in Sec. IV; comments added
in the conclusions of Sec. IV. v3: References added; some clarifications
added as footnotes 4 and 6, and in Sec. 3. Matches version accepted for
publication in JCA
Non-Gaussianity in the Cosmic Microwave Background Anisotropies at Recombination in the Squeezed limit
We estimate analytically the second-order cosmic microwave background
temperature anisotropies at the recombination epoch in the squeezed limit and
we deduce the contamination to the primordial local non-Gaussianity. We find
that the level of contamination corresponds to f_NL^{con}=O(1) which is below
the sensitivity of present experiments and smaller than the value O(5) recently
claimed in the literature.Comment: LaTeX file; 15 pages. Slightly revised version. Main result unchange
Primordial Bispectrum Information from CMB Polarization
After the precise observations of the Cosmic Microwave Background (CMB)
anisotropy power spectrum, attention is now being focused on the higher order
statistics of the CMB anisotropies. Since linear evolution preserves the
statistical properties of the initial conditions, observed non-Gaussianity of
the CMB will mirror primordial non-Gaussianity. Single field slow-roll
inflation robustly predicts negligible non-Gaussianity so an indication of
non-Gaussianity will suggest alternative scenarios need to be considered. In
this paper we calculate the information on primordial non-Gaussianity encoded
in the polarization of the CMB. After deriving the optimal weights for a cubic
estimator we evaluate the Signal-to-Noise ratio of the estimator for WMAP,
Planck and an ideal cosmic variance limited experiment. We find that when the
experiment can observe CMB polarization with good sensitivity, the sensitivity
to primordial non-Gaussianity increases by roughly a factor of two. We also
test the weakly non-Gaussian assumption used to derive the optimal weight
factor by calculating the degradation factor produced by the gravitational
lensing induced connected four-point function. The physical scales in the
radiative transfer functions are largely irrelevant for the constraints on the
primordial non-Gaussianity. We show that the total (S/N)^2 is simply
proportional to the number of observed pixels on the sky.Comment: To be submitted to PRD, 25 pages, 6 figure
Phase transition in the Countdown problem
Here we present a combinatorial decision problem, inspired by the celebrated
quiz show called the countdown, that involves the computation of a given target
number T from a set of k randomly chosen integers along with a set of
arithmetic operations. We find that the probability of winning the game
evidences a threshold phenomenon that can be understood in the terms of an
algorithmic phase transition as a function of the set size k. Numerical
simulations show that such probability sharply transitions from zero to one at
some critical value of the control parameter, hence separating the algorithm's
parameter space in different phases. We also find that the system is maximally
efficient close to the critical point. We then derive analytical expressions
that match the numerical results for finite size and permit us to extrapolate
the behavior in the thermodynamic limit.Comment: Submitted for publicatio
Infinitesimal and local convexity of a hypersurface in a semi-Riemannian manifold
Given a Riemannian manifold M and a hypersurface H in M, it is well known
that infinitesimal convexity on a neighborhood of a point in H implies local
convexity. We show in this note that the same result holds in a semi-Riemannian
manifold. We make some remarks for the case when only timelike, null or
spacelike geodesics are involved. The notion of geometric convexity is also
reviewed and some applications to geodesic connectedness of an open subset of a
Lorentzian manifold are given.Comment: 14 pages, AMSLaTex, 2 figures. v2: typos fixed, added one reference
and several comments, statement of last proposition correcte
Electromagnetic field fluctuations near a dielectric-vacuum boundary and surface divergences in the ideal conductor limit
We consider the electric and magnetic field fluctuations in the vacuum state
in the region external to a half-space filled with a homogeneous
non-dissipative dielectric. We discuss an appropriate limit to an ideal metal
and concentrate our interest on the renormalized field fluctuations, or
equivalently to renormalized electric and magnetic energy densities, in the
proximity of the dielectric-vacuum interface. We show that surface divergences
of field fluctuations arise at the interface in an appropriate ideal conductor
limit, and that our limiting procedure allows to discuss in detail their
structure. Field fluctuations close to the surface can be investigated through
the retarded Casimir-Polder interaction with an appropriate polarizable body.Comment: 6 pages, 2 figure
The consistency condition for the three-point function in dissipative single-clock inflation
We generalize the consistency condition for the three-point function in
single field inflation to the case of dissipative, multi-field, single-clock
models. We use the recently introduced extension of the effective field theory
of inflation that accounts for dissipative effects, to provide an explicit
proof to leading (non-trivial) order in the generalized slow roll parameters
and mixing with gravity scales. Our results illustrate the conditions necessary
for the validity of the consistency relation in situations with many degrees of
freedom relevant during inflation, namely that there is a preferred clock.
Departures from this condition in forthcoming experiments would rule out not
only single field but also a large class of multi-field models.Comment: 26+11 page
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