Infrared exponents of Yang-Mills theory

In this talk I summarise recent results on the infrared exponents of SU($N_c$)-Yang-Mills theory. I discuss a self-consistent power law solution for the Dyson-Schwinger equations for general 1PI-Greens functions in the infrared. The corresponding running coupling has a fixed point at zero momentum, which turns out to be universal and gauge invariant within a class of transverse gauges. When calculated on a torus the infrared exponents of the ghost and gluon propagators differ from the corresponding continuum solutions. They agree, however, well with results from lattice calculations.Comment: 6 pages, 3 figures, talk presented at Lattice2005(Topology and Confinement), Dublin, July 25-30, 2005. v2: reference adde

Analytic structure of the Landau gauge gluon propagator

The analytic structure of the non-perturbative gluon propagator contains information on the absence of gluons from the physical spectrum of the theory. We study this structure from numerical solutions in the complex momentum plane of the gluon and ghost Dyson-Schwinger equations in Landau gauge Yang-Mills theory. The resulting ghost and gluon propagators are analytic apart from a distinct cut structure on the real, timelike momentum axis. The propagator violates the Osterwalder-Schrader positivity condition, confirming the absence of gluons from the asymptotic spectrum of the theory.Comment: 5 pages, 7 figure

Turbulence, amalgamation and generic automorphisms of homogeneous structures

We study topological properties of conjugacy classes in Polish groups, with emphasis on automorphism groups of homogeneous countable structures. We first consider the existence of dense conjugacy classes (the topological Rokhlin property). We then characterize when an automorphism group admits a comeager conjugacy class (answering a question of Truss) and apply this to show that the homeomorphism group of the Cantor space has a comeager conjugacy class (answering a question of Akin-Hurley-Kennedy). Finally, we study Polish groups that admit comeager conjugacy classes in any dimension (in which case the groups are said to admit ample generics). We show that Polish groups with ample generics have the small index property (generalizing results of Hodges-Hodkinson-Lascar-Shelah) and arbitrary homomorphisms from such groups into separable groups are automatically continuous. Moreover, in the case of oligomorphic permutation groups, they have uncountable cofinality and the Bergman property. These results in particular apply to automorphism groups of many $\omega$-stable, $\aleph_0$-categorical structures and of the random graph. In this connection, we also show that the infinite symmetric group $S_\infty$ has a unique non-trivial separable group topology. For several interesting groups we also establish Serre's properties (FH) and (FA)

A Density-Based Approach to the Retrieval of Top-K Spatial Textual Clusters

Keyword-based web queries with local intent retrieve web content that is relevant to supplied keywords and that represent points of interest that are near the query location. Two broad categories of such queries exist. The first encompasses queries that retrieve single spatial web objects that each satisfy the query arguments. Most proposals belong to this category. The second category, to which this paper's proposal belongs, encompasses queries that support exploratory user behavior and retrieve sets of objects that represent regions of space that may be of interest to the user. Specifically, the paper proposes a new type of query, namely the top-k spatial textual clusters (k-STC) query that returns the top-k clusters that (i) are located the closest to a given query location, (ii) contain the most relevant objects with regard to given query keywords, and (iii) have an object density that exceeds a given threshold. To compute this query, we propose a basic algorithm that relies on on-line density-based clustering and exploits an early stop condition. To improve the response time, we design an advanced approach that includes three techniques: (i) an object skipping rule, (ii) spatially gridded posting lists, and (iii) a fast range query algorithm. An empirical study on real data demonstrates that the paper's proposals offer scalability and are capable of excellent performance