Statefinder hierarchy exploration of the extended Ricci dark energy

We apply the statefinder hierarchy plus the fractional growth parameter to explore the extended Ricci dark energy (ERDE) model, in which there are two independent coefficients $\alpha$ and $\beta$. By adjusting them, we plot evolution trajectories of some typical parameters, including Hubble expansion rate $E$, deceleration parameter $q$, the third and fourth order hierarchy $S_3^{(1)}$ and $S_4^{(1)}$ and fractional growth parameter $\epsilon$, respectively, as well as several combinations of them. For the case of variable $\alpha$ and constant $\beta$, in the low-redshift region the evolution trajectories of $E$ are in high degeneracy and that of $q$ separate somewhat. However, the $\Lambda$CDM model is confounded with ERDE in both of these two cases. $S_3^{(1)}$ and $S_4^{(1)}$, especially the former, perform much better. They can differentiate well only varieties of cases within ERDE except $\Lambda$CDM in the low-redshift region. For high-redshift region, combinations $\{S_n^{(1)},\epsilon\}$ can break the degeneracy. Both of $\{S_3^{(1)},\epsilon\}$ and $\{S_4^{(1)},\epsilon\}$ have the ability to discriminate ERDE with $\alpha=1$ from $\Lambda$CDM, of which the degeneracy cannot be broken by all the before-mentioned parameters. For the case of variable $\beta$ and constant $\alpha$, $S_3^{(1)}(z)$ and $S_4^{(1)}(z)$ can only discriminate ERDE from $\Lambda$CDM. Nothing but pairs $\{S_3^{(1)},\epsilon\}$ and $\{S_4^{(1)},\epsilon\}$ can discriminate not only within ERDE but also ERDE from $\Lambda$CDM. Finally we find that $S_3^{(1)}$ is surprisingly a better choice to discriminate within ERDE itself, and ERDE from $\Lambda$CDM as well, rather than $S_4^{(1)}$.Comment: 8 pages, 14 figures; published versio

QCD phase transitions via a refined truncation of Dyson-Schwinger equations

We investigate both the chiral and deconfinement phase transitions of QCD matter in a refined scheme of Dyson-Schwinger equations, which have been shown to be successful in giving the meson mass spectrum and matching the interaction with the results from ab initio computation. We verify the equivalence of the chiral susceptibility criterion with different definitions for the susceptibility and confirm that the chiral susceptibility criterion is efficient to fix not only the chiral phase boundary but also the critical end point (CEP), especially when one could not have the effective thermodynamical potential. We propose a generalized Schwinger function criterion for the confinement. We give the phase diagram of both phase transitions and show that in the refined scheme the position of the CEP shifts to lower chemical potential and higher temperature. Based on our calculation and previous results of the chemical freeze out conditions, we propose that the CEP locates in the states of the matter generated by the Au--Au collisions with $\sqrt{s_{NN}^{}}=9\sim15$ GeV.Comment: 12 pages, 6 figures, 1 tabl

Interface Effect in QCD Phase Transitions via Dyson-Schwinger Equation Approach

With the chiral susceptibility criterion we obtain the phase diagram of strong-interaction matter in terms of temperature and chemical potential in the framework of Dyson-Schwinger equations (DSEs) of QCD.After calculating the pressure and some other thermodynamic properties of the matter in the DSE method, we get the phase diagram in terms of temperature and baryon number density. We also obtain the interface tension and the interface entropy density to describe the inhomogeneity of the two phases in the coexistence region of the first order phase transition. After including the interface effect, we find that the total entropy density of the system increases in both the deconfinement (dynamical chiral symmetry restoration) and the hadronization (dynamical chiral symmetry breaking) processes of the first order phase transitions and thus solve the entropy puzzle in the hadronization process.Comment: 9 pages, 9 figures, and 1 tabl

Efficient information collection in stochastic optimisation

This thesis focuses on a class of information collection problems in stochastic optimisation. Algorithms in this area often need to measure the performances of several potential solutions, and use the collected information in their search for high-performance solutions, but only have a limited budget for measuring. A simple approach that allocates simulation time equally over all potential solutions may waste time in collecting additional data for the alternatives that can be quickly identified as non-promising. Instead, algorithms should amend their measurement strategy to iteratively examine the statistical evidences collected thus far and focus computational efforts on the most promising alternatives. This thesis develops new efficient methods of collecting information to be used in stochastic optimisation problems. First, we investigate an efficient measurement strategy used for the solution selection procedure of two-stage linear stochastic programs. In the solution selection procedure, finite computational resources must be allocated among numerous potential solutions to estimate their performances and identify the best solution. We propose a two-stage sampling approach that exploits a Wasserstein-based screening rule and an optimal computing budget allocation technique to improve the efficiency of obtaining a high-quality solution. Numerical results show our method provides good trade-offs between computational effort and solution performance. Then, we address the information collection problems that are encountered in the search for robust solutions. Specifically, we use an evolutionary strategy to solve a class of simulation optimisation problems with computationally expensive blackbox functions. We implement an archive sample approximation method to ix reduce the required number of evaluations. The main challenge in the application of this method is determining the locations of additional samples drawn in each generation to enrich the information in the archive and minimise the approximation error. We propose novel sampling strategies by using the Wasserstein metric to estimate the possible benefit of a potential sample location on the approximation error. An empirical comparison with several previously proposed archive-based sample approximation methods demonstrates the superiority of our approaches. In the final part of this thesis, we propose an adaptive sampling strategy for the rollout algorithm to solve the clinical trial scheduling and resource allocation problem under uncertainty. The proposed sampling strategy method exploits the variance reduction technique of common random numbers and the empirical Bernstein inequality in a statistical racing procedure, which can balance the exploration and exploitation of the rollout algorithm. Moreover, we present an augmented approach that utilises a heuristic-based grouping rule to enhance the simulation efficiency by breaking down the overall action selection problem into a selection problem involving small groups. The numerical results show that the proposed method provides competitive results within a reasonable amount of computational time

A Universal Constraint on the Infrared Behavior of the Ghost Propagator in QCD

With proposing a unified description of the fields variation at the level of generating functional, we obtain a new identity for the quark-gluon interaction vertex based on gauge symmetry, which is similar to the Slavnov-Taylor Identities(STIs) based on the Becchi-Rouet-Stora-Tyutin transformation. With these identities, we find that in Landau gauge, the dressing function of the ghost propagator approaches to a constant as its momentum goes to zero, which provides a strong constraint on the infrared behaviour of ghost propagator.Comment: 4 pages, no figur