35,744 research outputs found
Average Symmetry and Complexity of Binary Sequences
The concept of complexity as average symmetry is here formalised by
introducing a general expression dependent on the relevant symmetry and a
related discrete set of transformations. This complexity has hybrid features of
both statistical complexities and of those related to algorithmic complexity.
Like the former, random objects are not the most complex while they still are
more complex than the more symmetric ones (as in the latter). By applying this
definition to the particular case of rotations of binary sequences, we are able
to find a precise expression for it. In particular, we then analyse the
behaviour of this measure in different well-known automatic sequences, where we
find interesting new properties. A generalisation of the measure to statistical
ensembles is also presented and applied to the case of i.i.d. random sequences
and to the equilibrium configurations of the one-dimensional Ising model. In
both cases, we find that the complexity is continuous and differentiable as a
function of the relevant parameters and agrees with the intuitive requirements
we were looking for.Comment: 9 pages, 5 figure
Interactive mixture of inhomogeneous dark fluids driven by dark energy: a dynamical systems analysis
We examine the evolution of an inhomogeneous mixture of non-relativistic
pressureless cold dark matter (CDM), coupled to dark energy (DE) characterised
by the equation of state parameter , with the interaction term
proportional to the DE density. This coupled mixture is the source of a
spherically symmetric Lema\^\ itre-Tolman-Bondi (LTB) metric admitting an
asymptotic Friedman-Lema\^\ itre-Robertson-Walker (FLRW) background. Einstein's
equations reduce to a 5-dimensional autonomous dynamical system involving
quasi--local variables related to suitable averages of covariant scalars and
their fluctuations. The phase space evolution around the critical points
(past/future attractors and five saddles) is examined in detail. For all
parameter values and both directions of energy flow (CDM to DE and DE to CDM)
the phase space trajectories are compatible with a physically plausible early
cosmic times behaviour near the past attractor. This result compares favourably
with mixtures with the interaction driven by the CDM density in which
conditions for a physically plausible past evolution are more restrictive.
Numerical examples are provided describing the evolution of an initial profile
that can be associated with idealised structure formation scenariosComment: 23 pages, IOP format, 8 figure
On the weakness of disc models in bright ULXs
It is sometimes suggested that phenomenological power-law plus cool
disc-blackbody models represent the simplest, most robust interpretation of the
X-ray spectra of bright ultraluminous X-ray sources (ULXs); this has been taken
as evidence for the presence of intermediate-mass black holes (BHs) (M ~ 10^3
Msun) in those sources. Here, we assess this claim by comparing the cool
disc-blackbody model with a range of other models. For example, we show that
the same ULX spectra can be fitted equally well by subtracting a disc-blackbody
component from a dominant power-law component, thus turning a soft excess into
a soft deficit. Then, we propose a more complex physical model, based on a
power-law component slightly modified at various energies by smeared emission
and absorption lines from highly-ionized, fast-moving gas. We use the
XMM-Newton/EPIC spectra of two ULXs in Holmberg II and NGC 4559 as examples.
Our main conclusion is that the presence of a soft excess or a soft deficit
depends on the energy range over which we choose to fit the ``true'' power-law
continuum; those small deviations from the power-law spectrum are well modelled
by disc-blackbody components (either in emission or absorption) simply because
they are a versatile fitting tool for most kinds of smooth, broad bumps. Hence,
we argue that those components should not be taken as evidence for accretion
disc emission, nor used to infer BH masses. Finally, we speculate that bright
ULXs could be in a spectral state similar to (or an extension of) the
steep-power-law state of Galactic BH candidates, in which the disc is now
completely comptonized and not directly detectable, and the power-law emission
may be modified by the surrounding, fast-moving, ionized gas.Comment: 12 pages, accepted by MNRA
HART EFFECT AND EQUILIBRIUM IN INCOMPLETE MARKETS I
In this paper I reconsider the problem of the existence for GEI models. It is well known that existence for this kind of models can fail since there are bad spot prices. Using tools from Algebraic Geometry I show that the set of bad spot prices is tipically empty if the information tree, the number of secruities and the number of tradable goods at each node satisfy a well defined inequality. Even if such inequality is not staisfied I show that the set of bad spot price can be fully characterized and described using an algorithm and I give an universal bound for the cardinality of this set. Moreover, using these results, I prove that the equilibrium always exists for all endowment profiles.
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