Spatial dependence of gain nonlinearities in InGaAs semiconductor optical amplifier

Counter-propagating sub-picosecond pulses are used to monitor gain saturation along the waveguide of an InGaAs superlattice semiconductor optical amplifier at 1550 nm wavelength. The functional form of the spatial dependence of gain saturation is found to depend on pulse energy. These observations are interpreted by combining the optical nonlinearities associated with interband carrier dynamics and carrier heating together and their respective time constants. We show that the results are consistent with the predictions of a propagation model. Implications for all-optical switching, particularly in the limit of full saturation across the whole amplifier, are discussed. (c) 2005 American Institute of Physics.</p

The Kervaire-Laudenbach conjecture and presentations of simple groups

The statement ``no nonabelian simple group can be obtained from a nonsimple group by adding one generator and one relator" 1) is equivalent to the Kervaire--Laudenbach conjecture; 2) becomes true under the additional assumption that the initial nonsimple group is either finite or torsion-free. Key words: Kervaire--Laudenbach conjecture, relative presentations, simple groups, car motion, cocar comotion. AMS MSC: 20E32, 20F05, 20F06.Comment: 20 pages, 13 figure

The structure of one-relator relative presentations and their centres

Suppose that G is a nontrivial torsion-free group and w is a word in the alphabet G\cup\{x_1^{\pm1},...,x_n^{\pm1}\} such that the word w' obtained from w by erasing all letters belonging to G is not a proper power in the free group F(x_1,...,x_n). We show how to reduce the study of the relative presentation \^G= to the case n=1. It turns out that an "n-variable" group \^G can be constructed from similar "one-variable" groups using an explicit construction similar to wreath product. As an illustration, we prove that, for n>1, the centre of \^G is always trivial. For n=1, the centre of \^G is also almost always trivial; there are several exceptions, and all of them are known.Comment: 15 pages. A Russian version of this paper is at http://mech.math.msu.su/department/algebra/staff/klyachko/papers.htm . V4: the intoduction is rewritten; Section 1 is extended; a short introduction to Secton 5 is added; some misprints are corrected and some cosmetic improvements are mad

Community detection in temporal multilayer networks, with an application to correlation networks

Networks are a convenient way to represent complex systems of interacting entities. Many networks contain "communities" of nodes that are more densely connected to each other than to nodes in the rest of the network. In this paper, we investigate the detection of communities in temporal networks represented as multilayer networks. As a focal example, we study time-dependent financial-asset correlation networks. We first argue that the use of the "modularity" quality function---which is defined by comparing edge weights in an observed network to expected edge weights in a "null network"---is application-dependent. We differentiate between "null networks" and "null models" in our discussion of modularity maximization, and we highlight that the same null network can correspond to different null models. We then investigate a multilayer modularity-maximization problem to identify communities in temporal networks. Our multilayer analysis only depends on the form of the maximization problem and not on the specific quality function that one chooses. We introduce a diagnostic to measure \emph{persistence} of community structure in a multilayer network partition. We prove several results that describe how the multilayer maximization problem measures a trade-off between static community structure within layers and larger values of persistence across layers. We also discuss some computational issues that the popular "Louvain" heuristic faces with temporal multilayer networks and suggest ways to mitigate them.Comment: 42 pages, many figures, final accepted version before typesettin

Potassium condensing tests of horizontal multitube convective and radiative condensers operating at vapor temperatures of 1250 deg to 1500 deg F

Potassium condensing tests of horizontal multitube convective and radiative condenser operating at vapor temperature

Temporal Evolution of Financial Market Correlations

We investigate financial market correlations using random matrix theory and principal component analysis. We use random matrix theory to demonstrate that correlation matrices of asset price changes contain structure that is incompatible with uncorrelated random price changes. We then identify the principal components of these correlation matrices and demonstrate that a small number of components accounts for a large proportion of the variability of the markets that we consider. We then characterize the time-evolving relationships between the different assets by investigating the correlations between the asset price time series and principal components. Using this approach, we uncover notable changes that occurred in financial markets and identify the assets that were significantly affected by these changes. We show in particular that there was an increase in the strength of the relationships between several different markets following the 2007--2008 credit and liquidity crisis.Comment: 15 pages, 10 figures, 1 table. Accepted for publication in Phys. Rev. E. v2 includes additional section

Phylogenetic relationships of the Wolbachia of nematodes and arthropods

Wolbachia are well known as bacterial symbionts of arthropods, where they are reproductive parasites, but have also been described from nematode hosts, where the symbiotic interaction has features of mutualism. The majority of arthropod Wolbachia belong to clades A and B, while nematode Wolbachia mostly belong to clades C and D, but these relationships have been based on analysis of a small number of genes. To investigate the evolution and relationships of Wolbachia symbionts we have sequenced over 70 kb of the genome of wOvo, a Wolbachia from the human-parasitic nematode Onchocerca volvulus, and compared the genes identified to orthologues in other sequenced Wolbachia genomes. In comparisons of conserved local synteny, we find that wBm, from the nematode Brugia malayi, and wMel, from Drosophila melanogaster, are more similar to each other than either is to wOvo. Phylogenetic analysis of the protein-coding and ribosomal RNA genes on the sequenced fragments supports reciprocal monophyly of nematode and arthropod Wolbachia. The nematode Wolbachia did not arise from within the A clade of arthropod Wolbachia, and the root of the Wolbachia clade lies between the nematode and arthropod symbionts. Using the wOvo sequence, we identified a lateral transfer event whereby segments of the Wolbachia genome were inserted into the Onchocerca nuclear genome. This event predated the separation of the human parasite O. volvulus from its cattle-parasitic sister species, O. ochengi. The long association between filarial nematodes and Wolbachia symbionts may permit more frequent genetic exchange between their genomes

Community Structure in Time-Dependent, Multiscale, and Multiplex Networks

Network science is an interdisciplinary endeavor, with methods and applications drawn from across the natural, social, and information sciences. A prominent problem in network science is the algorithmic detection of tightly-connected groups of nodes known as communities. We developed a generalized framework of network quality functions that allowed us to study the community structure of arbitrary multislice networks, which are combinations of individual networks coupled through links that connect each node in one network slice to itself in other slices. This framework allows one to study community structure in a very general setting encompassing networks that evolve over time, have multiple types of links (multiplexity), and have multiple scales.Comment: 31 pages, 3 figures, 1 table. Includes main text and supporting material. This is the accepted version of the manuscript (the definitive version appeared in Science), with typographical corrections included her