Open-Universe Weighted Model Counting

Weighted model counting (WMC) has recently emerged as an effective and general approach to probabilistic inference, offering a computational framework for encoding a variety of formalisms, such as factor graphs and Bayesian networks.The advent of large-scale probabilistic knowledge bases has generated further interest in relational probabilistic representations, obtained by according weights to first-order formulas, whose semantics is given in terms of the ground theory, and solved by WMC. A fundamental limitation is that the domain of quantification, by construction and design, is assumed to be finite, which is at odds with areas such as vision and language understanding, where the existence of objects must be inferred from raw data. Dropping the finite-domain assumption has been known to improve the expressiveness of a first-order language for open-universe purposes, but these languages, so far, have eluded WMC approaches. In this paper, we revisit relational probabilistic models over an infinite domain, and establish a number of results that permit effective algorithms. We demonstrate this language on a number of examples, including a parameterized version of Pearl's Burglary-Earthquake-Alarm Bayesian network

Streaming Verification of Graph Properties

Streaming interactive proofs (SIPs) are a framework for outsourced computation. A computationally limited streaming client (the verifier) hands over a large data set to an untrusted server (the prover) in the cloud and the two parties run a protocol to confirm the correctness of result with high probability. SIPs are particularly interesting for problems that are hard to solve (or even approximate) well in a streaming setting. The most notable of these problems is finding maximum matchings, which has received intense interest in recent years but has strong lower bounds even for constant factor approximations. In this paper, we present efficient streaming interactive proofs that can verify maximum matchings exactly. Our results cover all flavors of matchings (bipartite/non-bipartite and weighted). In addition, we also present streaming verifiers for approximate metric TSP. In particular, these are the first efficient results for weighted matchings and for metric TSP in any streaming verification model.Comment: 26 pages, 2 figure, 1 tabl

Multifractal Analysis of Packed Swiss Cheese Cosmologies

The multifractal spectrum of various three-dimensional representations of Packed Swiss Cheese cosmologies in open, closed, and flat spaces are measured, and it is determined that the curvature of the space does not alter the associated fractal structure. These results are compared to observational data and simulated models of large scale galaxy clustering, to assess the viability of the PSC as a candidate for such structure formation. It is found that the PSC dimension spectra do not match those of observation, and possible solutions to this discrepancy are offered, including accounting for potential luminosity biasing effects. Various random and uniform sets are also analyzed to provide insight into the meaning of the multifractal spectrum as it relates to the observed scaling behaviors.Comment: 3 latex files, 18 ps figure

Negative vacuum energy densities and the causal diamond measure

Arguably a major success of the landscape picture is the prediction of a small, non-zero vacuum energy density. The details of this prediction depends in part on how the diverging spacetime volume of the multiverse is regulated, a question that remains unresolved. One proposal, the causal diamond measure, has demonstrated many phenomenological successes, including predicting a distribution of positive vacuum energy densities in good agreement with observation. In the string landscape, however, the vacuum energy density is expected to take positive and negative values. We find the causal diamond measure gives a poor fit to observation in such a landscape -- in particular, 99.6% of observers in galaxies seemingly just like ours measure a vacuum energy density smaller than we do, most of them measuring it to be negative.Comment: 9 pages, 3 figures; v2: minor error fixed (results essentially unchanged), reference added; v3: published version, includes a few clarification

A Reanalysis of Small Scale Velocity Dispersion in the CfA1 Survey

The velocity dispersion of galaxies on scales of $r\sim1h^{-1}$ Mpc, $\sigma_{12}(r)$, may be estimated from the anisotropy of the galaxy-galaxy correlation function in redshift space. We present a reanalysis of the CfA1 survey, correct an error in the original analysis of Davis and Peebles (1983), and find that $\sigma_{12}(r)$ is extremely sensitive to the details of how corrections for infall into the Virgo cluster are applied. We conclude that a robust value of $\sigma_{12}$ cannot be obtained from this survey. We also discuss results from other redshift surveys, including the effect of removing clusters.Comment: 12 pages, uuencoded(latex file + 2 Postscript figures), uses aas macro

Cosmology of the Lifshitz universe

We study the ultraviolet complete non-relativistic theory recently proposed by Horava. After introducing a Lifshitz scalar for a general background, we analyze the cosmology of the model in Lorentzian and Euclidean signature. Vacuum solutions are found and it is argued the existence of non-singular bouncing profiles. We find a general qualitative agreement with both the picture of Causal Dynamical Triangulations and Quantum Einstein Gravity. However, inflation driven by a Lifshitz scalar field on a classical background might not produce a scale-invariant spectrum when the principle of detailed balance is assumed.Comment: 23 pages. v2: one reference and one equation added, main conclusions unchanged; v3: matches published version, discussion improved, typos correcte

Hurdles for Recent Measures in Eternal Inflation

In recent literature on eternal inflation, a number of measures have been introduced which attempt to assign probabilities to different pocket universes by counting the number of each type of pocket according to a specific procedure. We give an overview of the existing measures, pointing out some interesting connections and generic predictions. For example, pairs of vacua that undergo fast transitions between themselves will be strongly favored. The resultant implications for making predictions in a generic potential landscape are discussed. We also raise a number of issues concerning the types of transitions that observers in eternal inflation are able to experience.Comment: 15 PRD-style pages, 5 figures, expanded discussion of measures in Sec. II, added reference