Cosmological perturbations in Horava-Lifshitz theory without detailed balance

In the Horava-Lifshitz theory of quantum gravity, two conditions -- detailed balance and projectability -- are usually assumed. The breaking of projectability simplifies the theory, but it leads to serious problems with the theory. The breaking of detailed balance leads to a more complicated form of the theory, but it appears to resolve some of the problems. Sotiriou, Visser and Weinfurtner formulated the most general theory of Horava-Lifshitz type without detailed balance. We compute the linear scalar perturbations of the FRW model in this form of HL theory. We show that the higher-order curvature terms in the action lead to a gravitational effective anisotropic stress on small scales. Specializing to a Minkowski background, we study the spin-0 scalar mode of the graviton, using a gauge-invariant analysis, and find that it is stable in both the infrared and ultraviolet regimes for $0 \le \xi \le 2/3$. However, in this parameter range the scalar mode is a ghost.Comment: Some typos were corrected. Verison appeared in Phys. Rev. D81, 024009 (2010

Decomposability for stable processes

We characterize all possible independent symmetric alpha-stable (SaS) components of an SaS process, 0<alpha<2. In particular, we focus on stationary SaS processes and their independent stationary SaS components. We also develop a parallel characterization theory for max-stable processes.Comment: Major revision. Section 4 of previous version removed due to a mistake in the proof. Remarks 3.2 and 3.3 adde

Ground and excited states of Li−^-, Be−^- through a density-based approach

Density functional calculations are performed for ground [He]2s$^2$ $^1$S$^e$, and three metastable bound excited states, 1s2s2p$^2$ $^5$P$^e$, 1s2p$^3$ $^5$S$^o$, 1s2s2p3p $^5$P$^e$ of Li$^-$ and [He]2s2p$^2$ $^4$P$^e$, [He]2p$^3$ $^4$S$^o$, 1s2s2p$^3$ $^6$S$^o$ of Be$^-$ each. The work-function-based exchange potential is used, while the correlation effects are included by employing the Lee-Yang-Parr potential. The relevant nonrelativistic KS equation is solved by means of a generalized pseudospectral discretization scheme offering nonuniform and optimal spatial grid. Computed total energies, radial densities, selected density moments, as well as two transition wavelengths (1s2s2p$^2$ $^5$P$^e \to$1s2p$^3$ $^5$S$^o$ of Li$^-$, [He]2s2p$^2$ $^4$P$^e \to$ [He]2p$^3$ $^4$S$^o$ of Be$^-$) show reasonably good agreement with the available theoretical and experimental data. The term energies show an absolute deviation of 0.007--0.171% with the largest deviation being observed for the even-parity $^5$P state of Li$^-$. The transition wavelengths of Li$^-$, Be$^-$ are calculated within 0.891 and 0.438% of the experimental values. This offers a simple practical route towards accurate reliable calculation of excited states of anions within density functional theory.Comment: 12 pages, 35 ref

Relaxations for inference in restricted Boltzmann machines

We propose a relaxation-based approximate inference algorithm that samples near-MAP configurations of a binary pairwise Markov random field. We experiment on MAP inference tasks in several restricted Boltzmann machines. We also use our underlying sampler to estimate the log-partition function of restricted Boltzmann machines and compare against other sampling-based methods.Comment: ICLR 2014 workshop track submissio