Initial energy density and gluon distribution from the Glasma in heavy-ion collisions

We estimate the energy density and the gluon distribution associated with the classical fields describing the early-time dynamics of the heavy-ion collisions. We first decompose the energy density into the momentum components exactly in the McLerran-Venugopalan model, with the use of the Wilson line correlators. Then we evolve the energy density with the free-field equation, which is justified by the dominance of the ultraviolet modes near the collision point. We also discuss the improvement with inclusion of nonlinear terms into the time evolution. Our numerical results at RHIC energy are fairly consistent with the empirical values.Comment: 14 pages, 8 figures, 3 table

Two-color quark matter: U(1)_A restoration, superfluidity, and quarkyonic phase

We discuss the phase structure of quantum chromodynamics (QCD) with two colors and two flavors of light quarks. This is motivated by the increasing interest in the QCD phase diagram as follows: (1) The QCD critical point search has been under intensive dispute and its location and existence suffer from uncertainty of effective U(1)_A symmetry restoration. (2) A new phase called quarkyonic matter is drawing theoretical and experimental attention but it is not clear whether it can coexist with diquark condensation. We point out that two-color QCD is nontrivial enough to contain essential ingredients for (1) and (2) both, and most importantly, is a system without the sign problem in numerical simulations on the lattice. We adopt the two-flavor Nambu-Jona-Lasinio model extended with the two-color Polyakov loop and make quantitative predictions which can be tested by lattice simulations.Comment: 14 pages, REVTeX4, 12 eps figures; v2: version published in Phys. Rev. D; v3: an error in the Appendix fixed, Fig. 9 modified accordingl

Are Muslims the New Catholics? Europe’s Headscarf Laws in Comparative Historical Perspective

In this paper a biologically-inspired model for partly occluded patterns is proposed. The model is based on the hypothesis that in human visual system occluding patterns play a key role in recognition as well as in reconstructing internal representation for a pattern’s occluding parts. The proposed model is realized with a bidirectional hierarchical neural network. In this network top-down cues, generated by direct connections from the lower to higher levels of hierarchy, interact with the bottom-up information, generated from the un-occluded parts, to recognize occluded patterns. Moreover, positional cues of the occluded as well as occluding patterns, that are computed separately but in the same network, modulate the top-down and bottom-up processing to reconstruct the occluded patterns. Simulation results support the presented hypothesis as well as effectiveness of the model in providing a solution to recognition of occluded patterns. The behavior of the model is in accordance to the known human behavior on the occluded patterns

Views of the Chiral Magnetic Effect

My personal views of the Chiral Magnetic Effect are presented, which starts with a story about how we came up with the electric-current formula and continues to unsettled subtleties in the formula. There are desirable features in the formula of the Chiral Magnetic Effect but some considerations would lead us to even more questions than elucidations. The interpretation of the produced current is indeed very non-trivial and it involves a lot of confusions that have not been resolved.Comment: 19 pages, no figure; typos corrected, references significantly updated, to appear in Lect. Notes Phys. "Strongly interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Ye

Heavy quark potential in the instanton liquid model

We study the heavy quark potential in the instanton liquid model by carefully measuring Wilson loops out to a distance of order 3$fm$. A random instanton ensemble with a fixed radius $\rho$ = 1/3$fm$ generates a potential $V(R)$ growing very slowly at large $R$. In contrast, a more realistic size distribution growing as $\rho^6$ at small $\rho$ and decaying as $\rho^{-5}$ at large $\rho$, leads to a potential which grows linearly with $R$. The string tension, however, is only about 1/10 of the phenomenological value.Comment: LATTICE98(confine

Second-order and Fluctuation-induced First-order Phase Transitions with Functional Renormalization Group Equations

We investigate phase transitions in scalar field theories using the functional renormalization group (RG) equation. We analyze a system with U(2)xU(2) symmetry, in which there is a parameter $\lambda_2$ that controls the strength of the first-order phase transition driven by fluctuations. In the limit of \lambda_2\to0$, the U(2)xU(2) theory is reduced to an O(8) scalar theory that exhibits a second-order phase transition in three dimensions. We develop a new insight for the understanding of the fluctuation-induced first-order phase transition as a smooth continuation from the standard RG flow in the O(8) system. In our view from the RG flow diagram on coupling parameter space, the region that favors the first-order transition emerges from the unphysical region to the physical one as \lambda_2 increases from zero. We give this interpretation based on the Taylor expansion of the functional RG equations up to the fourth order in terms of the field, which encompasses the$\epsilon$-expansion results. We compare results from the expansion and from the full numerical calculation and find that the fourth-order expansion is only of qualitative use and that the sixth-order expansion improves the quantitative agreement.Comment: 15 pages, 10 figures, major revision; discussions on O(N) models reduced, a summary section added after Introduction, references added; to appear in PR

Invariant, super and quasi-martingale functions of a Markov process

We identify the linear space spanned by the real-valued excessive functions of a Markov process with the set of those functions which are quasimartingales when we compose them with the process. Applications to semi-Dirichlet forms are given. We provide a unifying result which clarifies the relations between harmonic, co-harmonic, invariant, co-invariant, martingale and co-martingale functions, showing that in the conservative case they are all the same. Finally, using the co-excessive functions, we present a two-step approach to the existence of invariant probability measures

Are You Tampering With My Data?

We propose a novel approach towards adversarial attacks on neural networks (NN), focusing on tampering the data used for training instead of generating attacks on trained models. Our network-agnostic method creates a backdoor during training which can be exploited at test time to force a neural network to exhibit abnormal behaviour. We demonstrate on two widely used datasets (CIFAR-10 and SVHN) that a universal modification of just one pixel per image for all the images of a class in the training set is enough to corrupt the training procedure of several state-of-the-art deep neural networks causing the networks to misclassify any images to which the modification is applied. Our aim is to bring to the attention of the machine learning community, the possibility that even learning-based methods that are personally trained on public datasets can be subject to attacks by a skillful adversary.Comment: 18 page