134,094 research outputs found
Longitudinal flow and onset of deconfinement
The effects of the onset of deconfinement on longitudinal and transverse flow
are studied. First, we analyze longitudinal pion spectra from
GeV to GeV within Landau's hydrodynamical model and the
UrQMD transport approach. From the measured data on the widths of the pion
rapidity spectra, we extract the sound velocity in the early stage of
the reactions. It is found that the sound velocity has a local minimum
(indicating a softest point in the equation of state, EoS) at GeV. This softening of the EoS is compatible with the assumption of
the formation of a mixed phase at the onset of deconfinement. Furthermore, the
energy excitation function of elliptic flow () from MeV
to GeV is explored within the UrQMD framework and
discussed in the context of the available data. The transverse flow should also
be sensitive to changes in the equation of state. Therefore, the
underestimation of elliptic flow by the UrQMD model calculation above GeV might also be explained by assuming a phase transition from a
hadron gas to the quark gluon plasma around this energy. This would be
consistent with the model calculations, indicating a transition from hadronic
matter to ``string matter'' in this energy range.Comment: Proceedings of the 3rd International Workshop The Critical Point and
Onset of Deconfinement, Firenze, Ital
On the Convergence Speed of MDL Predictions for Bernoulli Sequences
We consider the Minimum Description Length principle for online sequence
prediction. If the underlying model class is discrete, then the total expected
square loss is a particularly interesting performance measure: (a) this
quantity is bounded, implying convergence with probability one, and (b) it
additionally specifies a `rate of convergence'. Generally, for MDL only
exponential loss bounds hold, as opposed to the linear bounds for a Bayes
mixture. We show that this is even the case if the model class contains only
Bernoulli distributions. We derive a new upper bound on the prediction error
for countable Bernoulli classes. This implies a small bound (comparable to the
one for Bayes mixtures) for certain important model classes. The results apply
to many Machine Learning tasks including classification and hypothesis testing.
We provide arguments that our theorems generalize to countable classes of
i.i.d. models.Comment: 17 page
Stochastic domination for the Ising and fuzzy Potts models
We discuss various aspects concerning stochastic domination for the Ising
model and the fuzzy Potts model. We begin by considering the Ising model on the
homogeneous tree of degree , \Td. For given interaction parameters ,
and external field h_1\in\RR, we compute the smallest external field
such that the plus measure with parameters and dominates
the plus measure with parameters and for all .
Moreover, we discuss continuity of with respect to the three
parameters , , and also how the plus measures are stochastically
ordered in the interaction parameter for a fixed external field. Next, we
consider the fuzzy Potts model and prove that on \Zd the fuzzy Potts measures
dominate the same set of product measures while on \Td, for certain parameter
values, the free and minus fuzzy Potts measures dominate different product
measures. For the Ising model, Liggett and Steif proved that on \Zd the plus
measures dominate the same set of product measures while on \T^2 that
statement fails completely except when there is a unique phase.Comment: 22 pages, 5 figure
Twisted Witt Groups of Flag Varieties
Calm\`es and Fasel have shown that the twisted Witt groups of split flag
varieties vanish in a large number of cases. For flag varieties over
algebraically closed fields, we sharpen their result to an if-and-only-if
statement. In particular, we show that the twisted Witt groups vanish in many
previously unknown cases. In the non-zero cases, we find that the twisted total
Witt group forms a free module of rank one over the untwisted total Witt group,
up to a difference in grading.
Our proof relies on an identification of the Witt groups of flag varieties
with the Tate cohomology groups of their K-groups, whereby the verification of
all assertions is eventually reduced to the computation of the (twisted) Tate
cohomology of the representation ring of a parabolic subgroup.Comment: inverse Cartan coefficients for E_7 in Figures 1, 2 and 3 corrected;
related mistake in the marking scheme for diagrams of type E_n corrected;
many minor corrections and clarifications; more example
South-South cooperation as piggy back for Brazil-Africa relations
https://www.researchgate.net/publication/292762698_South-South_Cooperation_As_Piggy_Back_For_Brazil-Africa_RelationsPublished versio
New error bounds for Solomonoff prediction
Solomonoff sequence prediction is a scheme to predict digits of binary strings without knowing the underlying probability distribution. We call a prediction scheme informed when it knows the true probability distribution of the sequence. Several new relations between universal Solomonoff sequence prediction and informed prediction and general probabilistic prediction schemes will be proved. Among others, they show that the number of errors in Solomonoff prediction is finite for computable distributions, if finite in the informed case. Deterministic variants will also be studied. The most interesting result is that the deterministic variant of Solomonoff prediction is optimal compared to any other probabilistic or deterministic prediction scheme apart from additive square root corrections only. This makes it well suited even for difficult prediction problems, where it does not suffice when the number of errors is minimal to within some factor greater than one. Solomonoff's original bound and the ones presented here complement each other in a useful way
- …