8,276 research outputs found
Comparing holographic dark energy models with statefinder
We apply the statefinder diagnostic to the holographic dark energy models,
including the original holographic dark energy (HDE) model, the new holographic
dark energy model, the new agegraphic dark energy (NADE) model, and the Ricci
dark energy model. In the low-redshift region the holographic dark energy
models are degenerate with each other and with the CDM model in the
and evolutions. In particular, the HDE model is highly degenerate
with the CDM model, and in the HDE model the cases with different
parameter values are also in strong degeneracy. Since the observational data
are mainly within the low-redshift region, it is very important to break this
low-redshift degeneracy in the and diagnostics by using some
quantities with higher order derivatives of the scale factor. It is shown that
the statefinder diagnostic is very useful in breaking the low-redshift
degeneracies. By employing the statefinder diagnostic the holographic dark
energy models can be differentiated efficiently in the low-redshift region. The
degeneracy between the holographic dark energy models and the CDM
model can also be broken by this method. Especially for the HDE model, all the
previous strong degeneracies appearing in the and diagnostics are
broken effectively. But for the NADE model, the degeneracy between the cases
with different parameter values cannot be broken, even though the statefinder
diagnostic is used. A direct comparison of the holographic dark energy models
in the -- plane is also made, in which the separations between the models
(including the CDM model) can be directly measured in the light of the
current values of the models.Comment: 8 pages, 8 figures; accepted by European Physical Journal C; matching
the publication versio
Statefinder hierarchy exploration of the extended Ricci dark energy
We apply the statefinder hierarchy plus the fractional growth parameter to
explore the extended Ricci dark energy (ERDE) model, in which there are two
independent coefficients and . By adjusting them, we plot
evolution trajectories of some typical parameters, including Hubble expansion
rate , deceleration parameter , the third and fourth order hierarchy
and and fractional growth parameter ,
respectively, as well as several combinations of them. For the case of variable
and constant , in the low-redshift region the evolution
trajectories of are in high degeneracy and that of separate somewhat.
However, the CDM model is confounded with ERDE in both of these two
cases. and , especially the former, perform much better.
They can differentiate well only varieties of cases within ERDE except
CDM in the low-redshift region. For high-redshift region, combinations
can break the degeneracy. Both of
and have the ability to
discriminate ERDE with from CDM, of which the degeneracy
cannot be broken by all the before-mentioned parameters. For the case of
variable and constant , and can
only discriminate ERDE from CDM. Nothing but pairs
and can discriminate not only
within ERDE but also ERDE from CDM. Finally we find that
is surprisingly a better choice to discriminate within ERDE itself, and ERDE
from CDM as well, rather than .Comment: 8 pages, 14 figures; published versio
Measuring the degree of unitarity for any quantum process
Quantum processes can be divided into two categories: unitary and non-unitary
ones. For a given quantum process, we can define a \textit{degree of the
unitarity (DU)} of this process to be the fidelity between it and its closest
unitary one. The DU, as an intrinsic property of a given quantum process, is
able to quantify the distance between the process and the group of unitary
ones, and is closely related to the noise of this quantum process. We derive
analytical results of DU for qubit unital channels, and obtain the lower and
upper bounds in general. The lower bound is tight for most of quantum
processes, and is particularly tight when the corresponding DU is sufficiently
large. The upper bound is found to be an indicator for the tightness of the
lower bound. Moreover, we study the distribution of DU in random quantum
processes with different environments. In particular, The relationship between
the DU of any quantum process and the non-markovian behavior of it is also
addressed.Comment: 7 pages, 2 figure
Revisiting the holographic dark energy in a non-flat universe: alternative model and cosmological parameter constraints
We propose an alternative model for the holographic dark energy in a non-flat
universe. This new model differs from the previous one in that the IR length
cutoff is taken to be exactly the event horizon size in a non-flat
universe, which is more natural and theoretically/conceptually concordant with
the model of holographic dark energy in a flat universe. We constrain the model
using the recent observational data including the type Ia supernova data from
SNLS3, the baryon acoustic oscillation data from 6dF, SDSS-DR7, BOSS-DR11, and
WiggleZ, the cosmic microwave background data from Planck, and the Hubble
constant measurement from HST. In particular, since some previous studies have
shown that the color-luminosity parameter of supernovae is likely to
vary during the cosmic evolution, we also consider such a case that in
SNLS3 is time-varying in our data fitting. Compared to the constant
case, the time-varying case reduces the value of by about 35
and results in that deviates from a constant at about 5 level,
well consistent with the previous studies. For the parameter of the
holographic dark energy, the constant fit gives and
the time-varying fit yields . In addition, an open
universe is favored (at about 2) for the model by the current data.Comment: 8 pages, 4 figure
Optimising Flexibility of Temporal Problems with Uncertainty
Temporal networks have been applied in many autonomous systems.
In real situations, we cannot ignore the uncertain factors when
using those autonomous systems. Achieving robust schedules and
temporal plans by optimising flexibility to tackle the
uncertainty is the motivation of the thesis.
This thesis focuses on the optimisation problems of temporal
networks with uncertainty and controllable options in the field
of Artificial Intelligence Planning and Scheduling. The goal of
this thesis is to construct flexibility and robustness metrics
for temporal networks under the constraints of different levels
of controllability. Furthermore, optimising flexibility for
temporal plans and schedules to achieve robust solutions with
flexible executions.
When solving temporal problems with uncertainty, postponing
decisions according to the observations of uncertain events
enables flexible strategies as the solutions instead of fixed
schedules or plans. Among the three levels of controllability of
the Simple Temporal Problem with Uncertainty (STPU), a problem is
dynamically controllable if there is a successful dynamic
strategy such that every decision in it is made according to the
observations of past events.
In the thesis, we make the following contributions. (1) We
introduce an optimisation model for STPU based on the existing
dynamic controllability checking algorithms. Some flexibility and
robustness measures are introduced based on the model. (2) We
extend the definition and verification algorithm of dynamic
controllability to temporal problems with controllable discrete
variables and uncertainty, which is called Controllable
Conditional Temporal Problems with Uncertainty (CCTPU). An
entirely dynamically controllable strategy of CCTPU consists of
both temporal scheduling and variable assignments being
dynamically decided, which maximize the flexibility of the
execution. (3) We introduce optimisation models of CCTPU under
fully dynamic controllability. The optimisation models aim to
answer the questions how flexible, robust or controllable a
schedule or temporal plan is. The experiments show that making
decisions dynamically can achieve better objective values than
doing statically.
The thesis also contributes to the field of AI planning and
scheduling by introducing robustness metrics of temporal
networks, proposing an envelope-based algorithm that can check
dynamic controllability of temporal networks with uncertainty and
controllable discrete decisions, evaluating improvements from
making decisions strongly controllable to temporally dynamically
controllable and fully dynamically controllable and comparing the
runtime of different implementations to present the scalability
of dynamically controllable strategies
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