The Master Equation for Large Population Equilibriums

We use a simple N-player stochastic game with idiosyncratic and common noises to introduce the concept of Master Equation originally proposed by Lions in his lectures at the Coll\`ege de France. Controlling the limit N tends to the infinity of the explicit solution of the N-player game, we highlight the stochastic nature of the limit distributions of the states of the players due to the fact that the random environment does not average out in the limit, and we recast the Mean Field Game (MFG) paradigm in a set of coupled Stochastic Partial Differential Equations (SPDEs). The first one is a forward stochastic Kolmogorov equation giving the evolution of the conditional distributions of the states of the players given the common noise. The second is a form of stochastic Hamilton Jacobi Bellman (HJB) equation providing the solution of the optimization problem when the flow of conditional distributions is given. Being highly coupled, the system reads as an infinite dimensional Forward Backward Stochastic Differential Equation (FBSDE). Uniqueness of a solution and its Markov property lead to the representation of the solution of the backward equation (i.e. the value function of the stochastic HJB equation) as a deterministic function of the solution of the forward Kolmogorov equation, function which is usually called the decoupling field of the FBSDE. The (infinite dimensional) PDE satisfied by this decoupling field is identified with the \textit{master equation}. We also show that this equation can be derived for other large populations equilibriums like those given by the optimal control of McKean-Vlasov stochastic differential equations. The paper is written more in the style of a review than a technical paper, and we spend more time and energy motivating and explaining the probabilistic interpretation of the Master Equation, than identifying the most general set of assumptions under which our claims are true

Evaluation of the Safety and Immunogenicity of the RTS,S/AS01E Malaria Candidate Vaccine When Integrated in the Expanded Program of Immunization

Background. The RTS,S/AS01E malaria candidate vaccine is being developed for immunization of African infants through the Expanded Program of Immunization (EPI). Methods. This phase 2, randomized, open, controlled trial conducted in Ghana, Tanzania, and Gabon evaluated the safety and immunogenicity of RTS,S/AS01E when coadministered with EPI vaccines. Five hundred eleven infants were randomized to receive RTS,S/AS01E at 0, 1, and 2 months (in 3 doses with diphtheria, tetanus, and wholecell pertussis conjugate [DTPw]; hepatitis B [HepB]; Haemophilus influenzae type b [Hib]; and oral polio vaccine [OPV]), RTS,S/AS01E at 0, 1, and 7 months (2 doses with DTPwHepB/Hib+OPV and 1 dose with measles and yellow fever), or EPI vaccines only. Results. The occurrences of serious adverse events were balanced across groups; none were vaccine-related. One child from the control group died. Mild to moderate fever and diaper dermatitis occurred more frequently in the RTS,S/AS01E coadministration groups. RTS,S/AS01E generated high anti-circumsporozoite protein and anti- hepatitis B surface antigen antibody levels. Regarding EPI vaccine responses upon coadministration when considering both immunization schedules, despite a tendency toward lower geometric mean titers to some EPI antigens, predefined noninferiority criteria were met for all EPI antigens except for polio 3 when EPI vaccines were given with RTS,S/AS01E at 0, 1, and 2 months. However, when antibody levels at screening were taken into account, the rates of response to polio 3 antigens were comparable between groups. Conclusion. RTS,S/AS01E integrated in the EPI showed a favorable safety and immunogenicity evaluation. Trial registration. ClinicalTrials.gov identifier: NCT00436007. GlaxoSmithKline study ID number: 106369 (Malaria-050

Investigating the NCQ scaling of elliptic flow at LHC with a multiphase transport model

The number of constituent quark (NCQ) scaling behavior of elliptic flow has been systematically studied at the LHC energy within the framework of a multiphase transport model (AMPT) in this work. We find that the parameters used to generate the initial states and the collision centrality are important for the existence of NCQ scaling even when hadronic rescattering contribution is off in Pb-Pb collisions of $\sqrt{s_{NN}}=2.76$ TeV. By turning on the hadron rescattering process, the hadronic evolution impacts are also found to be significant. Extending the analysis to Pb-Pb collsions of $\sqrt{s_{NN}}=5.02$ TeV, one would observe similar qualitative features

Coalescence Models For Hadron Formation From Quark Gluon Plasma

We review hadron formation from a deconfined quark gluon plasma (QGP) via coalescence or recombination of quarks and gluons. We discuss the abundant experimental evidence for coalescence from the Relativistic Heavy Ion Collider (RHIC) and compare the various coalescence models advocated in the literature. We comment on the underlying assumptions and remaining challenges as well as the merits of the models. We conclude with a discussion of some recent developments in the field.Comment: Review to appear in Annu. Rev. Nucl. Part. Sci. 58; 58 pages, 13 figures, 1 tabl

The QCD confinement transition: hadron formation

We review the foundations and the applications of the statistical and the quark recombination model as hadronization models.Comment: 45 pages, 16 figures, accepted for publication in Landolt-Boernstein Volume 1-23

Nucleon strangeness polarization from Λ/Λˉ\Lambda/\bar\Lambda hyperon production in polarized proton-proton collision at RHIC

We calculate the inclusive production of a polarized $\Lambda$ or $\bar{\Lambda}$ hyperon from the single longitudinally polarized proton and proton ($pp$) collision at RHIC. By comparing the data reported by the STAR Collaboration, we find that this process is sensitive to the polarization of strange and antistrange quarks of the proton in the experimental range. By introducing asymmetric coefficients with the minimization of $\chi^2$, we further identify the asymmetry of the polarized strange-antistrange quarks in the proton sea and find that the first moment is $\Delta s \approx -0.025\pm 0.019$ for strange quark and $\Delta\bar s \approx -0.001\pm 0.012$ for antistrange quark, with central values agreeing with the light-cone meson-baryon fluctuation model prediction, the recent lattice QCD determination of strangeness polarization and results from a global QCD analysis given by the Jefferson Lab Angular Momentum (JAM) Collaboration.Comment: 10 latex pages, 6 figures, final version for publicatio

Circumnuclear regions of different BPT types in star-forming MaNGA galaxies: AGN detectability

We consider the circumnuclear regions of MaNGA galaxies. The spectra are classified as AGN-like, HII-region-like (or SF-like), and intermediate (INT) spectra according to their positions on the BPT diagram. There are the following four configurations of the radiation distributions in the circumnuclear regions: 1) AGN+INT, the innermost region of the AGN-like radiation is surrounded by a ring of radiation of the intermediate type; 2) INT, the central area of radiation of the intermediate type; 3) SF+INT, the inner region of the HII-region-like radiation is surrounded by a ring of radiation of the intermediate type; and 4) SF, the HII-region-like radiation only. The LINERS of configurations 1 and 2 are examined. The spaxel spectra of the LINERs form a sequences on the BPT diagram. The line ratios change smoothly with radius, from AGN-like at the center to HII-region-like at larger distances. This is in agreement with the paradigm that the LINERs are excited by AGN activity. The AGN and INT radiation in the circumnuclear region is accompanied by an enhanced gas velocity dispersion, s_g. The radius of the area of the AGN and INT radiation is similar to the radius of the area with enhanced s_g, and the central s_g,c correlates with the luminosity of the AGN+INT area. We assume that the gas velocity dispersion can serve as an indicator of the AGN activity. The values of s_g,c for the SF-type centers partly overlap with those of the AGN-type centers. We find that there is a demarcation line between the positions of the AGN-type and SF-type objects on the s_g,c - central Halpha surface brightness diagram.Comment: 17 pages, 14 figures, accepted for publication in the A&