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 $E_{\rm lab}= 2A$ GeV to $\sqrt{s_{\rm NN}}=200$ 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 $c_s^2$ 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 $E_{\rm beam}=30A$ 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 ($v_2$) from $E_{\rm beam}=90A$ MeV to $\sqrt{s_{\rm NN}}=200$ 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 $E_{\rm lab}= 30A$ 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 $d$, \Td. For given interaction parameters $J_1$, $J_2>0$ and external field h_1\in\RR, we compute the smallest external field $\tilde{h}$ such that the plus measure with parameters $J_2$ and $h$ dominates the plus measure with parameters $J_1$ and $h_1$ for all $h\geq\tilde{h}$. Moreover, we discuss continuity of $\tilde{h}$ with respect to the three parameters $J_1$, $J_2$, $h$ 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

Progressive leaders see beyond themselves

https://www.researchgate.net/publication/292762579_Progressive_leaders_see_beyond_themselvesPublished versio

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

Frontier-markets bring all-new opportunities and challenges

https://www.researchgate.net/publication/292800824_Frontier_markets_bring_all-new_opportunities_and_challengesPublished 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

The Paradoxical Beauty of the Cross: Theological Aesthetics and the Doctrine of the Atonement in Athanasius’ Contra Gentes-De Incarnatio

In his two-part treatise Contra Gentes-De Incarnatio, Athanasius offers an interesting apologetic for the Christian doctrine of the atonement by employing various aesthetic themes and forms of expression drawn from the classical notion of beauty found particularly in the Platonic and neo-Platonic traditions. Although Athanasius never mentions the term “beauty” in Contra Gentes-De Incarnatio, the concept certainly looms in the background. Writing against the Platonic, Epicurean, and Stoic systems of his day, Athanasius centers his apologetic on the philosophical tension evident in the doctrine of divine transcendence/immanence. This paper argues that Athanasius implicitly characterizes the tension of divine transcendence/ immanence as paradoxical in nature and, as such, is not solved but resolved in Christian doctrine of the incarnation and the culminating event of the crucifixion. For Athanasius, the aesthetic force of the crucifixion is its manifold paradox in which Christ, the God-man, conquers by being conquered, restores man\u27s spiritual form by becoming formless, and establishes universal peace by surrendering to violence. Thus, in the Christian tradition, the divine transcendence/immanence paradox is localized and expanded in the incarnation and crucifixion event invoking an overflow of aesthetic inspiration in the heart of the believer. Therefore, the purpose of this essay is twofold. First, it will identify certain themes in the classical definition of beauty and will examine how these themes are interwoven throughout Athanasius’ apologetic . Second, it will attempt to prove that the aesthetic superiority of the cross, as implicitly argued in Contra Gentes-De Incarnatio, is rooted in the paradoxical nature of the crucifixion event. Thus, for Athanasius, beauty shines forth through paradox