2,754 research outputs found
Constraints on inflation revisited: An analysis including the latest local measurement of the Hubble constant
We revisit the constraints on inflation models by using the current
cosmological observations involving the latest local measurement of the Hubble
constant ( km s Mpc). We constrain the
primordial power spectra of both scalar and tensor perturbations with the
observational data including the Planck 2015 CMB full data, the BICEP2 and Keck
Array CMB B-mode data, the BAO data, and the direct measurement of . In
order to relieve the tension between the local determination of the Hubble
constant and the other astrophysical observations, we consider the additional
parameter in the cosmological model. We find that, for the
CDM++ model, the scale invariance is only excluded at
the 3.3 level, and is favored at the 1.6
level. Comparing the obtained 1 and 2 contours of
with the theoretical predictions of selected inflation models, we find that
both the convex and concave potentials are favored at 2 level, the
natural inflation model is excluded at more than 2 level, the
Starobinsky inflation model is only favored at around 2 level,
and the spontaneously broken SUSY inflation model is now the most favored
model.Comment: 10 pages, 6 figure
Constraining dark energy with Hubble parameter measurements: an analysis including future redshift-drift observations
Dark energy affects the Hubble expansion rate (namely, the expansion history)
by an integral over . However, the usual observables are the
luminosity distances or the angular diameter distances, which measure the
distance-redshift relation. Actually, dark energy affects the distances (and
the growth factor) by a further integration over functions of . Thus, the
direct measurements of the Hubble parameter at different redshifts are
of great importance for constraining the properties of dark energy. In this
paper, we show how the typical dark energy models, for example, the
CDM, CDM, CPL, and holographic dark energy (HDE) models, can be
constrained by the current direct measurements of (31 data in total,
covering the redshift range of ). In fact, the future
redshift-drift observations (also referred to as the Sandage-Loeb test) can
also directly measure at higher redshifts, covering the range of . We thus discuss what role the redshift-drift observations can play in
constraining dark energy with the Hubble parameter measurements. We show that
the constraints on dark energy can be improved greatly with the data
from only a 10-year observation of redshift drift.Comment: 20 pages, 5 figures; final version published in EPJ
Price-Based Resource Allocation for Spectrum-Sharing Femtocell Networks: A Stackelberg Game Approach
This paper investigates the price-based resource allocation strategies for
the uplink transmission of a spectrum-sharing femtocell network, in which a
central macrocell is underlaid with distributed femtocells, all operating over
the same frequency band as the macrocell. Assuming that the macrocell base
station (MBS) protects itself by pricing the interference from the femtocell
users, a Stackelberg game is formulated to study the joint utility maximization
of the macrocell and the femtocells subject to a maximum tolerable interference
power constraint at the MBS. Especially, two practical femtocell channel
models: sparsely deployed scenario for rural areas and densely deployed
scenario for urban areas, are investigated. For each scenario, two pricing
schemes: uniform pricing and non-uniform pricing, are proposed. Then, the
Stackelberg equilibriums for these proposed games are studied, and an effective
distributed interference price bargaining algorithm with guaranteed convergence
is proposed for the uniform-pricing case. Finally, numerical examples are
presented to verify the proposed studies. It is shown that the proposed
algorithms are effective in resource allocation and macrocell protection
requiring minimal network overhead for spectrum-sharing-based two-tier
femtocell networks.Comment: 27 pages, 7 figures, Submitted to JSA
Optimal Sparse Regression Trees
Regression trees are one of the oldest forms of AI models, and their
predictions can be made without a calculator, which makes them broadly useful,
particularly for high-stakes applications. Within the large literature on
regression trees, there has been little effort towards full provable
optimization, mainly due to the computational hardness of the problem. This
work proposes a dynamic-programming-with-bounds approach to the construction of
provably-optimal sparse regression trees. We leverage a novel lower bound based
on an optimal solution to the k-Means clustering algorithm in 1-dimension over
the set of labels. We are often able to find optimal sparse trees in seconds,
even for challenging datasets that involve large numbers of samples and
highly-correlated features.Comment: AAAI 2023, final archival versio
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