Thermodynamic properties and phase diagram of quark matter within non-extensive Polyakov chiral SU(3)quark mean field model

In the present study,we applied Tsallis non-extensive statistics to investigate the thermodynamic properties and phase diagram of quark matter in the Polyakov chiral SU(3)quark mean field model.Within this model,the properties of the quark matter were modified through the scalar fieldsσ,ζ,δ,χ,vector fieldsω,ρ,ϕ,and Polyakov fieldsΦandΦ¯at finite temperature and chemical potential.Non-extensive effects were introduced through a dimensionless parameter q,and the results were compared to those of the extensive case(q→1).In the non-extensive case,the exponential in the Fermi-Dirac(FD)function was modified to a q-exponential form.The influence of the q parameter on the thermodynamic properties,pressure,energy,and entropy density,as well as trace anomaly,was investigated.The speed of sound and specific heat with non-extensive effects were also studied.Furthermore,the effect of non-extensivity on the deconfinement phase transition as well as the chiral phase transition of u,d,and s quarks was explored.We found that the critical end point(CEP),which defines the point in the(T−μ)phase diagram where the order of the phase transition changes,shifts to a lower value of temperature,TCEP,and a higher value of chemical potential,μCEP,as the non-extensivity is increased,that is,q>1.

Sarve:synthetic data and local differential privacy for private frequency estimation

The collection of user attributes by service providers is a double-edged sword.They are instrumental in driving statistical analysis to train more accurate predictive models like recommenders.The analysis of the collected user data includes frequency estimation for categorical attributes.Nonetheless,the users deserve privacy guarantees against inadvertent identity disclosures.Therefore algorithms called frequency oracles were developed to randomize or perturb user attributes and estimate the frequencies of their values.We propose Sarve,a frequency oracle that used Randomized Aggregatable Privacy-Preserving Ordinal Response(RAPPOR)and Hadamard Response(HR)for randomization in combination with fake data.The design of a service-oriented architecture must consider two types of complexities,namely computational and communication.The functions of such systems aim to minimize the two complexities and therefore,the choice of privacy-enhancing methods must be a calculated decision.The variant of RAPPOR we had used was realized through bloom flters.A bloom filter is a memory-efficient data structure that offers time complexity of O(1).On the other hand,HR has been proven to give the best communication costs of the order of log(b)for b-bits communication.Therefore,Sarve is a step towards frequency oracles that exhibit how privacy provisions of existing methods can be combined with those of fake data to achieve statistical results comparable to the original data.Sarve also implemented an adaptive solution enhanced from the work of Arcolezi et al.The use of RAPPOR was found to provide better privacy-utility tradeoffs for specific privacy budgets in both high and general privacyregimes.