Constraints on Flows in Horava-Lifshitz Gravity by Classical Solutions

We find exact static stringy solutions of Horava-Lifshitz gravity with the projectability condition but imposing the detailed balance condition near the UV fixed point, and propose a method on constraining the possible pattern of flows in Horava-Lifshitz gravity by using the obtained classical solutions. In the obtained vacuum solutions, the parameters related to the speed of the graviton and the coefficients of quartic spatial derivative terms lead to intriguing effects: the change of graviton speed yields a surplus angle and the quartic derivatives make the square of effective electric charge negative. The result of a few tests based on the geometries of a cone, an excess cone, a black string, and a charged (black) string seems suggestive. For example, the flow of constant graviton speed and variable Newton's coupling can be favored in the vicinity of IR fixed point, but the conclusion is indistinct and far from definite yet. Together with the numerous classical solutions, static or time-dependent, which have already been found, the accumulated data from various future tests will give some hints in constraining the flow patterns more deterministic.Comment: 27 pages, 3 figures, version to appear in PR

Monopole Floer homology for rational homology 3-spheres

We give a new construction of monopole Floer homology for spin-c rational homology 3-spheres. As applications we define two invariants of certain smooth compact 4-manifolds with b_1=1 and b^+=0.Comment: 60 pages, to appear in Duke J. Math. v2: Minor improvements concerning orientations on pages 18-21. v3: Two new sections 4 and 14 have been added

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Department of Computer Science and EngineeringRecently deep reinforcement learning (DRL) algorithms show super human performances in the simulated game domains. In practical points, the sample efficiency is also one of the most important measures to determine the performance of a model. Especially for the environment of large search spaces (e.g. continuous action space), it is very critical condition to achieve the state-of-the-art performance. In this thesis, we design a model to be applicable to multi-end games in continuous space with high sample efficiency. A multi-end game has several sub-games which are independent each other but affect the result of the game by some rules of its domain. We verify the algorithm in the environment of simulated curling.clos

Gamma-Set Domination Graphs. I: Complete Biorientations of \u3cem\u3eq-\u3c/em\u3eExtended Stars and Wounded Spider Graphs

The domination number of a graph G, γ(G), and the domination graph of a digraph D, dom(D) are integrated in this paper. The γ-set domination graph of the complete biorientation of a graph G, domγ(G) is created. All γ-sets of specific trees T are found, and dom-γ(T) is characterized for those classes

Superdiffusive nonequilibrium motion of an impurity in a Fermi sea

We treat the nonequilibrium motion of a single impurity atom in a low-temperature single-species Fermi sea, interacting via a contact interaction. In the nonequilibrium regime, the impurity does a superdiffusive geometric random walk where the typical distance traveled grows with time as $\sim t^{d/(d+1)}$ for the $d$-dimensional system with $d\geq 2$. For nonzero temperature $T$, this crosses over to diffusive motion at long times with diffusivity $D\sim T^{-(d-1)/2}$. These results apply also to a nonzero concentration of impurity atoms as long as they remain dilute and nondegenerate.Comment: 5 pages, 1 figure, to appear in Phys. Rev.

Ballistic spreading of entanglement in a diffusive nonintegrable system

We study the time evolution of the entanglement entropy of a one-dimensional nonintegrable spin chain, starting from random nonentangled initial pure states. We use exact diagonalization of a nonintegrable quantum Ising chain with transverse and longitudinal fields to obtain the exact quantum dynamics. We show that the entanglement entropy increases linearly with time before finite-size saturation begins, demonstrating a ballistic spreading of the entanglement, while the energy transport in the same system is diffusive. Thus we explicitly demonstrate that the spreading of entanglement is much faster than the energy diffusion in this nonintegrable system.Comment: 7 pages, 7 figures. Published version. Supplementary material adde