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

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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

Equivariant aspects of Yang-Mills Floer theory

We use Floer's exact triangle to study the u-map (cup product with the 4-dimensional class) in the Floer cohomology groups of admissible SO(3) bundles over closed, oriented 3-manifolds. In the case of non-trivial bundles we show that (u^2-64)^n = 0 for some positive integer n. For homology 3-spheres Y the same holds for a certain reduced Floer group, which is obtained from the ordinary one by factoring out interaction with the trivial connection. This leads to a new proof (in the simply-connected case) of the finite type conjecture of Kronheimer and Mrowka concerning the structure of Donaldson polynomials. In the case of rational coefficients, interaction with the trivial connection is measured by a single integer h(Y), which is additive under connected sums and depends only on the rational homology cobordism class of Y.Comment: A few cosmetic changes. To appear in Topolog

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

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

Multivariate p-dic L-function

We construct multivariate p-adic L-function in the p-adic number fild by using Washington method.Comment: 9 page