Restricted Value Iteration: Theory and Algorithms

Value iteration is a popular algorithm for finding near optimal policies for POMDPs. It is inefficient due to the need to account for the entire belief space, which necessitates the solution of large numbers of linear programs. In this paper, we study value iteration restricted to belief subsets. We show that, together with properly chosen belief subsets, restricted value iteration yields near-optimal policies and we give a condition for determining whether a given belief subset would bring about savings in space and time. We also apply restricted value iteration to two interesting classes of POMDPs, namely informative POMDPs and near-discernible POMDPs

Towards efficient SimRank computation on large networks

SimRank has been a powerful model for assessing the similarity of pairs of vertices in a graph. It is based on the concept that two vertices are similar if they are referenced by similar vertices. Due to its self-referentiality, fast SimRank computation on large graphs poses significant challenges. The state-of-the-art work [17] exploits partial sums memorization for computing SimRank in O(Kmn) time on a graph with n vertices and m edges, where K is the number of iterations. Partial sums memorizing can reduce repeated calculations by caching part of similarity summations for later reuse. However, we observe that computations among different partial sums may have duplicate redundancy. Besides, for a desired accuracy ϵ, the existing SimRank model requires K = [logC ϵ] iterations [17], where C is a damping factor. Nevertheless, such a geometric rate of convergence is slow in practice if a high accuracy is desirable. In this paper, we address these gaps. (1) We propose an adaptive clustering strategy to eliminate partial sums redundancy (i.e., duplicate computations occurring in partial sums), and devise an efficient algorithm for speeding up the computation of SimRank to 0(Kdn2) time, where d is typically much smaller than the average in-degree of a graph. (2) We also present a new notion of SimRank that is based on a differential equation and can be represented as an exponential sum of transition matrices, as opposed to the geometric sum of the conventional counterpart. This leads to a further speedup in the convergence rate of SimRank iterations. (3) Using real and synthetic data, we empirically verify that our approach of partial sums sharing outperforms the best known algorithm by up to one order of magnitude, and that our revised notion of SimRank further achieves a 5X speedup on large graphs while also fairly preserving the relative order of original SimRank scores

LS 5039 - the counterpart of the unidentified MeV source GRO J1823-12

The COMPTEL experiment on CGRO observed the gamma-ray sky at energies from 0.75 MeV to 30 MeV between April 1991 and June 2000. COMPTEL detected many gamma-ray sources, among them an unidentified one labeled GRO J1823-12, which is positionally consistent with the prominent high-mass X-ray binary LS 5039. Because LS 5039 was established as gamma-ray emitter during recent years, whose gamma-radiation radiation is modulated along its binary orbit, we reanalysed the COMPTEL data of GRO J1823-12 including an orbital resolved analysis. We find a significant MeV source, showing evidence for a modulated MeV flux corresponding to the orbital period of LS 5039 of about 3.9 days. We show that its MeV emission is stronger at the orbital part around the inferior conjuction than at the part of the superior conjunction, being in phase with X-rays and TeV gamma-rays, however being in anti-phase with GeV gamma-rays. We conclude that the COMPTEL source GRO J1823-12 is the counterpart of the microquasar candidate LS 5039, at least for the majority of its MeV emission. The COMPTEL fluxes, put into multifrequency perspective, provide new constraints on the modelling of the high-energy emission of LS 5039.Comment: accepted by Astronomy & Astrophysics; 11 pages, 9 figure

Fe/Ni ratio in the Ant Nebula Mz 3

We have analyzed the [Fe II] and [Ni II] emission lines in the bipolar planetary nebula Mz~3. We find that the [Fe II] and [Ni II] lines arise exclusively from the central regions. Fluorescence excitation in the formation process of these lines is negligible for this low-excitation nebula. From the [Fe II]/[Ni II] ratio, we obtain a higher Fe/Ni abundance ratio with respect to the solar value. The current result provides further supporting evidence for Mz 3 as a symbiotic Mira.Comment: 2 pages, 1 figure, to be published in the Proceedings of the IAU Symposium 234: Planetary Nebulae in Our Galaxy and Beyond, eds. M.J. Barlow, R.H. Mende