Clustered Graph Coloring and Layered Treewidth

A graph coloring has bounded clustering if each monochromatic component has bounded size. This paper studies clustered coloring, where the number of colors depends on an excluded complete bipartite subgraph. This is a much weaker assumption than previous works, where typically the number of colors depends on an excluded minor. This paper focuses on graph classes with bounded layered treewidth, which include planar graphs, graphs of bounded Euler genus, graphs embeddable on a fixed surface with a bounded number of crossings per edge, amongst other examples. Our main theorem says that for fixed integers $s,t,k$, every graph with layered treewidth at most $k$ and with no $K_{s,t}$ subgraph is $(s+2)$-colorable with bounded clustering. In the $s=1$ case, which corresponds to graphs of bounded maximum degree, we obtain polynomial bounds on the clustering. This greatly improves a corresponding result of Esperet and Joret for graphs of bounded genus. The $s=3$ case implies that every graph with a drawing on a fixed surface with a bounded number of crossings per edge is 5-colorable with bounded clustering. Our main theorem is also a critical component in two companion papers that study clustered coloring of graphs with no $K_{s,t}$-subgraph and excluding a fixed minor, odd minor or topological minor

π\pi-J/ψJ/\psi Correlation and Elliptic Flow Parameter v2v_2 of Charmed Mesons at RHIC Energy

We study the correlation between the trigger $\pi$ and the associated $J/\psi$ on near and away sides in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV. In the region of trigger momentum $p_t>4$ GeV/$c$, the $\pi$ spectrum is composed of thermal-shower and shower-shower recombinations in the frame work of the recombination model. We consider the azimuthal anisotropy in the quenched hard parton distribution and then calculate the elliptic flow parameter $v_2$ of charmed mesons ($J/\psi$, $D^0$ and $D_s$) for different centralities.Comment: 17 pages, 6 figure

Non-linear excitations in 1D correlated insulators

In this work we investigate charge transport in one-dimensional (1D) insulators via semi-classical and perturbative renormalization group (RG) methods. We consider the problem of electron-electron, electron-phonon and electron-two-level system interactions. We show that non-linear collective modes such as polarons and solitons are reponsible for transport. We find a new excitation in the Mott insulator: the polaronic soliton. We discuss the differences between band and Mott insulators in terms of their spin spectrum and obtain the charge and spin gaps in each one of these systems. We show that electron-electron interactions provide strong renormalizations of the energy scales in the problem.Comment: 29 page

CoreTSAR: Task Scheduling for Accelerator-aware Runtimes

Heterogeneous supercomputers that incorporate computational accelerators such as GPUs are increasingly popular due to their high peak performance, energy efficiency and comparatively low cost. Unfortunately, the programming models and frameworks designed to extract performance from all computational units still lack the flexibility of their CPU-only counterparts. Accelerated OpenMP improves this situation by supporting natural migration of OpenMP code from CPUs to a GPU. However, these implementations currently lose one of OpenMP’s best features, its flexibility: typical OpenMP applications can run on any number of CPUs. GPU implementations do not transparently employ multiple GPUs on a node or a mix of GPUs and CPUs. To address these shortcomings, we present CoreTSAR, our runtime library for dynamically scheduling tasks across heterogeneous resources, and propose straightforward extensions that incorporate this functionality into Accelerated OpenMP. We show that our approach can provide nearly linear speedup to four GPUs over only using CPUs or one GPU while increasing the overall flexibility of Accelerated OpenMP