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In this proceeding we review our recent work using supervised learning with a deep convolutional neural network (CNN) to identify the QCD equation of state (EoS) employed in hydrodynamic modeling of heavy-ion collisions given only final-state particle spectra ρ(pT, Ф). We showed that there is a traceable encoder of the dynamical information from phase structure (EoS) that survives the evolution and exists in the final snapshot, which enables the trained CNN to act as an effective “EoS-meter” in detecting the nature of the QCD transition.
A primordial state of matter consisting of free quarks and gluons that existed in the early universe a few microseconds after the Big Bang is also expected to form in high-energy heavy-ion collisions. Determining the equation of state (EoS) of such a primordial matter is the ultimate goal of high-energy heavy-ion experiments. Here we use supervised learning with a deep convolutional neural network to identify the EoS employed in the relativistic hydrodynamic simulations of heavy ion collisions. High-level correlations of particle spectra in transverse momentum and azimuthal angle learned by the network act as an effective EoS-meter in deciphering the nature of the phase transition in quantum chromodynamics. Such EoS-meter is model-independent and insensitive to other simulation inputs including the initial conditions for hydrodynamic simulations.
The state-of-the-art pattern recognition method in machine learning (deep convolution neural network) is used to identify the equation of state (EoS) employed in the relativistic hydrodynamic simulations of heavy ion collisions. High-level correlations of particle spectra in transverse momentum and azimuthal angle learned by the network act as an effective EoS-meter in deciphering the nature of the phase transition in QCD. The EoS-meter is model independent and insensitive to other simulation inputs including the initial conditions and shear viscosity for hydrodynamic simulations. Through this study we demonstrate that there is a traceable encoder of the dynamical information from the phase structure that survives the evolution and exists in the final snapshot of heavy ion collisions and one can exclusively and effectively decode these information from the highly complex final output with machine learning when traditional methods fail. Besides the deep neural network, the performance of traditional machine learning classifiers are also provided.
A data-driven method was applied to Au+Au collisions at √sNN = 200 GeV made with the STAR detector at RHIC to isolate pseudorapidity distance η-dependent and η-independent correlations by using two- and four-particle azimuthal cumulant measurements. We identified a η-independent component of the correlation, which is dominated by anisotropic flow and flow fluctuations. It was also found to be independent of η within the measured range of pseudorapidity |η| < 1. In 20–30% central Au+Au collisions, the relative flow fluctuation was found to be 34%±2%(stat.)±3%(sys.) for particles with transverse momentum pT less than 2 GeV/c. The η-dependent part, attributed to nonflow correlations, is found to be 5% ± 2%(sys.) relative to the flow of the measured second harmonic cumulant at |η| > 0.7.
We compute the fermion spin distribution in the vortical fluid created in off-central high energy heavy-ion collisions. We employ the event-by-event (3+1)D viscous hydrodynamic model. The spin polarization density is proportional to the local fluid vorticity in quantum kinetic theory. As a result of strong collectivity, the spatial distribution of the local vorticity on the freeze-out hyper-surface strongly correlates to the rapidity and azimuthal angle distribution of fermion spins. We investigate the sensitivity of the local polarization to the initial fluid velocity in the hydrodynamic model and compute the global polarization of Λ hyperons by the AMPT model. The energy dependence of the global polarization agrees with the STAR data.
In the past two decades, pions created in the high density regions of heavy ion collisions have been predicted to be sensitive at high densities to the symmetry energy term in the nuclear equation of state, a property that is key to our understanding of neutron stars. In a new experiment designed to study the symmetry energy, the multiplicities of negatively and positively charged pions have been measured with high accuracy for central 132Sn+124Sn, 112Sn+124Sn, and 108Sn+112Sn collisions at E/A = 270 MeV with the SπRIT Time Projection Chamber. While individual pion multiplicities are measured to 4% accuracy, those of the charged pion multiplicity ratios are measured to 2% accuracy. We compare these data to predictions from seven major transport models. The calculations reproduce qualitatively the dependence of the multiplicities and their ratios on the total neutron and proton number in the colliding systems. However, the predictions of the transport models from different codes differ too much to allow extraction of reliable constraints on the symmetry energy from the data. This finding may explain previous contradictory conclusions on symmetry energy constraints obtained from pion data in Au+Au system. These new results call for still better understanding of the differences among transport codes, and new observables that are more sensitive to the density dependence of the symmetry energy.
Objectives: This study identified potential general influencing factors for a mathematical prediction of implant stability quotient (ISQ) values in clinical practice.
Methods: We collected the ISQ values of 557 implants from 2 different brands (SICace and Osstem) placed by 2 surgeons in 336 patients. Surgeon 1 placed 329 SICace implants, and surgeon 2 placed 113 SICace implants and 115 Osstem implants. ISQ measurements were taken at T1 (immediately after implant placement) and T2 (before dental restoration). A multivariate linear regression model was used to analyze the influence of the following 11 candidate factors for stability prediction: sex, age, maxillary/mandibular location, bone type, immediate/delayed implantation, bone grafting, insertion torque, I-stage or II-stage healing pattern, implant diameter, implant length and T1-T2 time interval.
Results: The need for bone grafting as a predictor significantly influenced ISQ values in all three groups at T1 (weight coefficients ranging from -4 to -5). In contrast, implant diameter consistently influenced the ISQ values in all three groups at T2 (weight coefficients ranging from 3.4 to 4.2). Other factors, such as sex, age, I/II-stage implantation and bone type, did not significantly influence ISQ values at T2, and implant length did not significantly influence ISQ values at T1 or T2.
Conclusions: These findings provide a rational basis for mathematical models to quantitatively predict the ISQ values of implants in clinical practice.
In this proceeding, we review our recent work using deep convolutional neural network (CNN) to identify the nature of the QCD transition in a hybrid modeling of heavy-ion collisions. Within this hybrid model, a viscous hydrodynamic model is coupled with a hadronic cascade “after-burner”. As a binary classification setup, we employ two different types of equations of state (EoS) of the hot medium in the hydrodynamic evolution. The resulting final-state pion spectra in the transverse momentum and azimuthal angle plane are fed to the neural network as the input data in order to distinguish different EoS. To probe the effects of the fluctuations in the event-by-event spectra, we explore different scenarios for the input data and make a comparison in a systematic way. We observe a clear hierarchy in the predictive power when the network is fed with the event-by-event, cascade-coarse-grained and event-fine-averaged spectra. The carefully-trained neural network can extract high-level features from pion spectra to identify the nature of the QCD transition in a realistic simulation scenario.
We present STAR measurements of charged hadron production as a function of centrality in Au+Au collisions at sqrt[sNN ]=130 GeV . The measurements cover a phase space region of 0.2< pT <6.0 GeV/c in transverse momentum and -1< eta <1 in pseudorapidity. Inclusive transverse momentum distributions of charged hadrons in the pseudorapidity region 0.5< | eta | <1 are reported and compared to our previously published results for | eta | <0.5 . No significant difference is seen for inclusive pT distributions of charged hadrons in these two pseudorapidity bins. We measured dN/d eta distributions and truncated mean pT in a region of pT > pcutT , and studied the results in the framework of participant and binary scaling. No clear evidence is observed for participant scaling of charged hadron yield in the measured pT region. The relative importance of hard scattering processes is investigated through binary scaling fraction of particle production.
We present data on e+ e- pair production accompanied by nuclear breakup in ultraperipheral gold-gold collisions at a center of mass energy of 200 GeV per nucleon pair. The nuclear breakup requirement selects events at small impact parameters, where higher-order diagrams for pair production should be enhanced. We compare the data with two calculations: one based on the equivalent photon approximation, and the other using lowest-order quantum electrodynamics (QED). The data distributions agree with both calculations, except that the pair transverse momentum spectrum disagrees with the equivalent photon approach. We set limits on higher-order contributions to the cross section.