Plane correlations and hydrodynamic simulations of heavy ion collisions

We use a nonlinear response formalism to describe the event plane correlations measured by the ATLAS collaboration. With one exception ($leftlangle cos(2Psi_2 - 6Psi_3 + 4 Psi_4) rightrangle$), the event plane correlations are qualitatively reproduced by considering the linear and quadratic response to the lowest cumulants. For the lowest harmonics such as $leftlangle cos(2Psi_2+3Psi_3 - 5Psi_5) rightrangle$, the correlations are quantitatively reproduced, even when the naive Glauber model prediction has the wrong sign relative to experiment. The quantitative agreement for the higher plane correlations (especially those involving $Psi_6$) is not as good. The centrality dependence of the correlations is naturally explained as an average of the linear and quadratic response.

Second order viscous corrections to the harmonic spectrum in heavy ion collisions

We calculate the second order viscous correction to the kinetic distribution, $delta f_{(2)}$, and use this result in a hydrodynamic simulation of heavy ion collisions to determine the complete second order correction to the harmonic spectrum, $v_n$. At leading order in a conformal fluid, the first viscous correction is determined by one scalar function, $chi_{0p}$. One moment of this scalar function is constrained by the shear viscosity. At second order in a conformal fluid, we find that $delta f(p)$ can be characterized by two scalar functions of momentum, $chi_{1p}$ and $chi_{2p}$. The momentum dependence of these functions is largely determined by the kinematics of the streaming operator. Again, one moment of these functions is constrained by the parameters of second order hydrodynamics, $tau_pi$ and $lambda_1$. The effect of $delta f_{(2)}$ on the integrated flow is small (up to $v_4$), but is quite important for the higher harmonics at modestly-large $p_T$. Generally, $delta f_{(2)}$ increases the value of $v_n$ at a given $p_T$, and is most important in small systems.

QCD and Relativistic $O(alpha_{s}v^2)$ Corrections to Hadronic Decays of Spin-Singlet Heavy Quarkonia $h_c, h_b$ and $eta_b$

We calculate the annihilation decay widths of spin-singlet heavy quarkonia $h_c, h_b$ and $eta_b$} into light hadrons with both QCD and relativistic corrections at order $O(alpha_{s}v^{2})$ in nonrelativistic QCD. With appropriate estimates for the long-distance matrix elements by using the potential model and operator evolution method, we find that our predictions of these decay widths are consistent with recent experimental measurements. We also find that the $O(alpha_{s}v^{2})$ corrections are small for $bbar{b}$ states but substantial for $cbar{c}$ states. In particular, the negative contribution of $O(alpha_{s}v^{2})$ correction to the $h_{c}$ decay can lower the decay width, as compared with previous predictions without the $O(alpha_{s}v^{2})$ correction, and thus result in a good agreement with the recent BESIII measurement.

Embedding Description Logic Programs into Default Logic

Description logic programs (dl-programs) under the answer set semantics formulated by Eiter {em et al.} have been considered as a prominent formalism for integrating rules and ontology knowledge bases. A question of interest has been whether dl-programs can be captured in a general formalism of nonmonotonic logic. In this paper, we study the possibility of embedding dl-programs into default logic. We show that dl-programs under the strong and weak answer set semantics can be embedded in default logic by combining two translations, one of which eliminates the constraint operator from nonmonotonic dl-atoms and the other translates a dl-program into a default theory. For dl-programs without nonmonotonic dl-atoms but with the negation-as-failure operator, our embedding is polynomial, faithful, and modular. In addition, our default logic encoding can be extended in a simple way to capture recently proposed weakly well-supported answer set semantics, for arbitrary dl-programs. These results reinforce the argument that default logic can serve as a fruitful foundation for query-based approaches to integrating ontology and rules. With its simple syntax and intuitive semantics, plus available computational results, default logic can be considered an attractive approach to integration of ontology and rules.

Triangularity and Dipole Asymmetry in Heavy Ion Collisions

We introduce a cumulant expansion to parameterize possible initial conditions in relativistic heavy ion collisions. We show that the cumulant expansion converges and that it can systematically reproduce the results of Glauber type initial conditions. At third order in the gradient expansion, the cumulants characterize the triangularity $<r^3 cos3(phi - psi_{3,3})>$ and the dipole asymmetry $<r^3 cos(phi- psi_{1,3})>$ of the initial entropy distribution. We show that for mid-peripheral collisions the orientation angle of the dipole asymmetry $psi_{1,3}$ has a $20%$ preference out of plane. This leads to a small net $v_1$ out of plane. In peripheral and mid-central collisions the orientation angles $psi_{1,3}$ and $psi_{3,3}$ are strongly correlated. We study the ideal hydrodynamic response to these cumulants and determine the associated $v_1/epsilon_1$ and $v_3/epsilon_3$ for a massless ideal gas equation of state. $v_1$ and $v_3$ develop towards the edge of the nucleus, and consequently the final spectra are more sensitive to the viscous dynamics of freezeout. The hydrodynamic calculations for $v_3$ are compared to Alver and Roland fit of two particle correlation functions. Finally, we propose to measure the $v_1$ associated with the dipole asymmetry and the correlations between $psi_{1,3}$ and $psi_{3,3}$ by measuring a two particle correlation with respect to the participant plane, $<cos(phi_a - 3phi_b + 2Psi_{PP})>$. The hydrodynamic prediction for this correlation function is several times larger than a correlation currently measured by the STAR collaboration, $<cos(phi_a + phi_b - 2Psi_{PP})>$.

Loop Formulas for Description Logic Programs

Description Logic Programs (dl-programs) proposed by Eiter et al. constitute an elegant yet powerful formalism for the integration of answer set programming with description logics, for the Semantic Web. In this paper, we generalize the notions of completion and loop formulas of logic programs to description logic programs and show that the answer sets of a dl-program can be precisely captured by the models of its completion and loop formulas. Furthermore, we propose a new, alternative semantics for dl-programs, called the {em canonical answer set semantics}, which is defined by the models of completion that satisfy what are called canonical loop formulas. A desirable property of canonical answer sets is that they are free of circular justifications. Some properties of canonical answer sets are also explored.

A Novel Clustering Algorithm Based on Quantum Games

Enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum game with the problem of data clustering, and then develop a quantum-game-based clustering algorithm, in which data points in a dataset are considered as players who can make decisions and implement quantum strategies in quantum games. After each round of a quantum game, each players expected payoff is calculated. Later, he uses a link-removing-and-rewiring (LRR) function to change his neighbors and adjust the strength of links connecting to them in order to maximize his payoff. Further, algorithms are discussed and analyzed in two cases of strategies, two payoff matrixes and two LRR functions. Consequently, the simulation results have demonstrated that data points in datasets are clustered reasonably and efficiently, and the clustering algorithms have fast rates of convergence. Moreover, the comparison with other algorithms also provides an indication of the effectiveness of the proposed approach.

A Novel Clustering Algorithm Based on Quantum Random Walk

The enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum random walk (QRW) with the problem of data clustering, and develop two clustering algorithms based on the one dimensional QRW. Then, the probability distributions on the positions induced by QRW in these algorithms are investigated, which also indicates the possibility of obtaining better results. Consequently, the experimental results have demonstrated that data points in datasets are clustered reasonably and efficiently, and the clustering algorithms are of fast rates of convergence. Moreover, the comparison with other algorithms also provides an indication of the effectiveness of the proposed approach.

A Novel Clustering Algorithm Based on a Modified Model of Random Walk

We introduce a modified model of random walk, and then develop two novel clustering algorithms based on it. In the algorithms, each data point in a dataset is considered as a particle which can move at random in space according to the preset rules in the modified model. Further, this data point may be also viewed as a local control subsystem, in which the controller adjusts its transition probability vector in terms of the feedbacks of all data points, and then its transition direction is identified by an event-generating function. Finally, the positions of all data points are updated. As they move in space, data points collect gradually and some separating parts emerge among them automatically. As a consequence, data points that belong to the same class are located at a same position, whereas those that belong to different classes are away from one another. Moreover, the experimental results have demonstrated that data points in the test datasets are clustered reasonably and efficiently, and the comparison with other algorithms also provides an indication of the effectiveness of the proposed algorithms.