Finitely generated soluble groups and their subgroups

We prove that every finitely generated soluble group which is not virtually abelian has a subgroup of one of a small number of types.Comment: 16 page

Topological structures in the equities market network

We present a new method for articulating scale-dependent topological descriptions of the network structure inherent in many complex systems. The technique is based on "Partition Decoupled Null Models,'' a new class of null models that incorporate the interaction of clustered partitions into a random model and generalize the Gaussian ensemble. As an application we analyze a correlation matrix derived from four years of close prices of equities in the NYSE and NASDAQ. In this example we expose (1) a natural structure composed of two interacting partitions of the market that both agrees with and generalizes standard notions of scale (eg., sector and industry) and (2) structure in the first partition that is a topological manifestation of a well-known pattern of capital flow called "sector rotation.'' Our approach gives rise to a natural form of multiresolution analysis of the underlying time series that naturally decomposes the basic data in terms of the effects of the different scales at which it clusters. The equities market is a prototypical complex system and we expect that our approach will be of use in understanding a broad class of complex systems in which correlation structures are resident.Comment: 17 pages, 4 figures, 3 table

A unifying representation for a class of dependent random measures

We present a general construction for dependent random measures based on thinning Poisson processes on an augmented space. The framework is not restricted to dependent versions of a specific nonparametric model, but can be applied to all models that can be represented using completely random measures. Several existing dependent random measures can be seen as specific cases of this framework. Interesting properties of the resulting measures are derived and the efficacy of the framework is demonstrated by constructing a covariate-dependent latent feature model and topic model that obtain superior predictive performance

FFTs for the 2-Sphere-Improvements and Variations

Earlier work by Driscoll and Healy has produced an efficient algorithm for computing the Fourier transform of band-limited functions on the 2-sphere. In this paper we present a reformulation and variation of the original algorithm which results in a greatly improved inverse transform, and consequent improved convolution algorithm for such functions. All require at most 0(N log2 N) operations where N is the number of sample points. We also address implementation considerations and give heuristics for allowing reliable floating point implementations of a slightly modified algorithm at little cost in either theoretical or actual performance. These claims are supported by extensive numerical experiments from our implementation in C on DEC and Sun workstations. These results give strong indications that the algorithm is both reliable and efficient for a large range of useful problem sizes. The paper concludes with a brief discussion of a few potential appications

Efficiency and Stability Issues in the Numerical Computation of Fourier Transforms and Convolutions on the 2-Sphere

Earlier work by Driscoll and Healy has produced an efficient algorithm for computing the Fourier transform of band-limited functions on the sphere. In this paper we present a greatly improved inverse transform, and consequent improved convolution algorithm for such functions. We also discuss implementational considerations and give heuristics for allowing reliable floating point implementations of a slightly modified algorithm at little cost in either theoretical or actual performance. This discussion is supplemented with numerical experiments from our implementation in C on a DecStation 5000. These results give strong indications that the algorithm is both reliable and efficient for a large range of useful problem sizes

Evolution of community structure in the world trade web

In this note we study the bilateral merchandise trade flows between 186 countries over the 1948-2005 period using data from the International Monetary Fund. We use Pajek to identify network structure and behavior across thresholds and over time. In particular, we focus on the evolution of trade "islands" in the a world trade network in which countries are linked with directed edges weighted according to fraction of total dollars sent from one country to another. We find mixed evidence for globalization.Comment: To be submitted to APFA 6 Proceedings, 8 pages, 3 Figure