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Although calculations of QCD thermodynamics from first-principle lattice simulations are limited to zero net-density due to the fermion sign problem, several methods have been developed to extend the equation of state (EoS) to finite values of theB,Q,Schemical potentials. Taylor expansion aroundµ_i=0 (i = B,Q,S) enables to cover with confidence the region up toµ_i/T< 2.5. Recently, a new method has been developed to compute a 2D EoS in the (T,µ_B) plane. It was constructed through aT-expansion scheme (TExS), based on a resummation of the Taylor expansion, and is trusted up to densities aroundµ_B/T= 3.5. We present here the new 4D-TExS EoS, a generalization of the TExS to all 3 chemical potentials, expected to offer a larger coverage than the 4D Taylor expansion EoS. After explaining the basics of theT-Expansion Scheme and how it is generalized to multiple dimensions, we will present results for thermodynamic observables as functions of temperature and both finite baryon and strangeness chemical potentials. 

Recently, seven produced hadron species have been used to construct multiple hadron sets with given differences in the net electric charge (∆q) and strangeness (∆S) between the two sides. A nonzero directed flow difference △v₁has been proposed as a consequence of the electromagnetic field produced in relativistic heavy ion collisions. Previously, we have shown with quark coalescence that Av1 and the slope difference △v′₁depend linearly on both △qand ∆Swith zero intercept. Here we emphasize that a two-dimensional function or fit is necessary for extracting the △q- and △S-dependences of △v₁. On the other hand, a one-dimensional fit gives a different value for the slope parameter of the ∆q- or ∆S-dependence. Furthermore, a one-dimensional fit is incorrect because its slope parameter depends on the arbitrary scaling factor of a hadron set and is thus ill-defined. We use test data of △v₁to explicitly demonstrate these points. 

We present a Bayesian analysis, based on holography and constrained by lattice QCD simulations, which leads to a prediction for the existence and location of the QCD critical point. We employ two different parametrizations of the functions that characterize the breaking of conformal invariance and the baryonic charge in the Einstein-Maxwell-dilaton holographic model. They lead to predictions for the critical point that overlap at one sigma. While some samples of the prior distribution do not predict a critical point, or produce critical points that cover large regions of the phase diagram, all posterior samples present a critical point at chemical potentials µBc~550-630 MeV.