Structure and Response in the World Trade Network

We examine how the structure of the world trade network has been shaped by globalization and recessions over the last 40 years. We show that by treating the world trade network as an evolving system, theory predicts the trade network is more sensitive to evolutionary shocks and recovers more slowly from them now than it did 40 years ago, due to structural changes in the world trade network induced by globalization. We also show that recession-induced change to the world trade network leads to an \emph{increased} hierarchical structure of the global trade network for a few years after the recession.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let

To perform a gyro test of general relativity in a satellite and develop associated control technology

Performance tests of gyroscope operations and gyroscope readout equipment are discussed. The gyroscope was tested for 400 hours at liquid helium temperatures with spin speeds up to 30 Hz. Readout by observing trapped magnetic flux in the spinning rotor with a sensitive magnetometer was accomplished. Application of the gyroscope to space probes and shuttle vehicles

On a conjecture of Bennewitz, and the behaviour of the Titchmarsh-Weyl matrix near a pole

For any real limit-$n$ $2n$th-order selfadjoint linear differential expression on $[0,\infty)$, Titchmarsh- Weyl matrices $M(\lambda)$ can be defined. Two matrices of particu lar interest are the matrices $M_D(\lambda)$ and $M_N(\lambda)$ assoc iated respectively with Dirichlet and Neumann boundary conditions at $x=0$. These satisfy $M_D(\lambda) = -M_{N}(\lambda)^{-1}$. It is known that when these matrices have poles (which can only lie on the real axis) the existence of valid HELP inequalities depends on their behaviour in the neighbourhood of these poles. We prove a conjecture of Bennewitz and use it, together with a new algorithm for computing the Laurent expansion of a Titchmarsh-Weyl matrix in the neighbourhood of a pole, to investigate the existence of HELP inequalities for a number of differential equations which have so far proved awkward to analys

Statistical Mechanics of Community Detection

Starting from a general \textit{ansatz}, we show how community detection can be interpreted as finding the ground state of an infinite range spin glass. Our approach applies to weighted and directed networks alike. It contains the \textit{at hoc} introduced quality function from \cite{ReichardtPRL} and the modularity $Q$ as defined by Newman and Girvan \cite{Girvan03} as special cases. The community structure of the network is interpreted as the spin configuration that minimizes the energy of the spin glass with the spin states being the community indices. We elucidate the properties of the ground state configuration to give a concise definition of communities as cohesive subgroups in networks that is adaptive to the specific class of network under study. Further we show, how hierarchies and overlap in the community structure can be detected. Computationally effective local update rules for optimization procedures to find the ground state are given. We show how the \textit{ansatz} may be used to discover the community around a given node without detecting all communities in the full network and we give benchmarks for the performance of this extension. Finally, we give expectation values for the modularity of random graphs, which can be used in the assessment of statistical significance of community structure

Hierarchical growing neural gas

“The original publication is available at www.springerlink.com”. Copyright Springer.This paper describes TreeGNG, a top-down unsupervised learning method that produces hierarchical classification schemes. TreeGNG is an extension to the Growing Neural Gas algorithm that maintains a time history of the learned topological mapping. TreeGNG is able to correct poor decisions made during the early phases of the construction of the tree, and provides the novel ability to influence the general shape and form of the learned hierarchy